With the passage of time, the 78-year-old former president’s speeches have grown darker, harsher, longer, angrier, less focused, more profane and increasingly fixated on the past, according to a review of his public appearances over the years.

Former President Donald J. Trump vividly recounted how the audience at his climactic debate with Vice President Kamala Harris was on his side. Except that there was no audience. The debate was held in an empty hall. No one “went crazy,” as Mr. Trump put it, because no one was there.

Anyone can misremember, of course. But the debate had been just a week earlier and a fairly memorable moment. And it was hardly the only time Mr. Trump has seemed confused, forgetful, incoherent or disconnected from reality lately. In fact, it happens so often these days that it no longer even generates much attention.

He rambles, he repeats himself, he roams from thought to thought — some of them hard to understand, some of them unfinished, some of them factually fantastical. He voices outlandish claims that seem to be made up out of whole cloth. He digresses into bizarre tangents about golf, about sharks, about his own “beautiful” body. He relishes “a great day in Louisiana” after spending the day in Georgia. He expresses fear that North Korea is “trying to kill me” when he presumably means Iran. As late as last month, Mr. Trump was still speaking as if he were running against President Biden, five weeks after his withdrawal from the race.

With Mr. Biden out, Mr. Trump, at 78, is now the oldest major party nominee for president in history and would be the oldest president ever if he wins and finishes another term at 82. A review of Mr. Trump’s rallies, interviews, statements and social media posts finds signs of change since he first took the political stage in 2015. He has always been discursive and has often been untethered to truth, but with the passage of time his speeches have grown darker, harsher, longer, angrier, less focused, more profane and increasingly fixated on the past.

According to a computer analysis by The New York Times, Mr. Trump’s rally speeches now last an average of 82 minutes, compared with 45 minutes in 2016. Proportionately, he uses 13 percent more all-or-nothing terms like “always” and “never” than he did eight years ago, which some experts consider a sign of advancing age.

Similarly, he uses 32 percent more negative words than positive words now, compared with 21 percent in 2016, which can be another indicator of cognitive change. And he uses swearwords 69 percent more often than he did when he first ran, a trend that could reflect what experts call disinhibition. (A study by Stat, a health care news outlet, produced similar findings.)

Mr. Trump frequently reaches to the past for his frame of reference, often to the 1980s and 1990s, when he was in his tabloid-fueled heyday. He cites fictional characters from that era like Hannibal Lecter from “Silence of the Lip” (he meant “Silence of the Lambs”), asks “where’s Johnny Carson, bring back Johnny” (who died in 2005) and ruminates on how attractive Cary Grant was (“the most handsome man”). He asks supporters whether they remember the landing in New York of Charles Lindbergh, who actually landed in Paris and long before Mr. Trump was born.

He seems confused about modern technology, suggesting that “most people don’t have any idea what the hell a phone app is” in a country where 96 percent of people own a smartphone. If sometimes he seems stuck in the 1990s, there are moments when he pines for the 1890s, holding out that decade as the halcyon period of American history and William McKinley as his model president because of his support for tariffs.

And he heads off into rhetorical cul-de-sacs. “So we built a thing called the Panama Canal,” he told the conservative host Tucker Carlson last year. “We lost 35,000 people to the mosquito, you know, malaria. We lost 35,000 people building — we lost 35,000 people because of the mosquito. Vicious. They had to build under nets. It was one of the true great wonders of the world. As he said, ‘One of the nine wonders of the world.’ No, no, it was one of the seven. It just happened a little while ago. You know, he says, ‘Nine wonders of the world.’ You could make nine wonders. He would’ve been better off if he stuck with the nine and just said, ‘Yeah, I think it’s nine.’”

While elements of this are familiar, some who have known him for years say they notice a change. “He’s not competing at the level he was competing at eight years ago, no question about it,” said Anthony Scaramucci, a former Trump ally who has endorsed Ms. Harris. “He’s lost a step. He’s lost an ability to put powerful sentences together.”

“You can like Trump or hate Trump, but he’s been a very effective communicator,” Mr. Scaramucci continued. But now, he added, “the word salad buffet on the Trump campaign is being offered at a discount. You can eat all you can eat, but it’s at a discount.”

Sarah Matthews, who was Mr. Trump’s deputy press secretary until breaking with him over the Jan. 6, 2021, attack, said the former president had lost his fastball.

“I don’t think anyone would ever say that Trump is the most polished speaker, but his more recent speeches do seem to be more incoherent, and he’s rambling even more so and he’s had some pretty noticeable moments of confusion,” she said. “When he was running against Biden, maybe it didn’t stand out as much.”

Mr. Trump dismisses any concerns and insists that he has passed cognitive tests. “I go for two hours without teleprompters, and if I say one word slightly out, they say, ‘He’s cognitively impaired,’” he complained at a recent rally. He calls his meandering style “the weave” and asserts that it is an intentional and “brilliant” communication strategy.

Steven Cheung, the campaign communications director, called Mr. Trump “the strongest and most capable candidate” and dismissed suggestions that he has diminished with age. “President Trump has more energy and more stamina than anyone in politics, and is the smartest leader this country has ever seen,” he said in a statement.

The former president has not been hobbled politically by his age as much as Mr. Biden was, in part because the incumbent comes across as physically frail while Mr. Trump still exudes energy. But his campaign has refused to release medical records, instead simply pointing to a one-page letter released in July by his former White House doctor reporting that Mr. Trump was “doing well” after being grazed by a bullet in an assassination attempt.

How much his rambling discourse — what some experts call tangentiality — can be attributed to age is the subject of some debate. Mr. Trump has always had a distinctive speaking style that entertained and captivated supporters even as critics called him detached from reality. Indeed, questions have been raised about Mr. Trump’s mental fitness for years.

John F. Kelly, his second White House chief of staff, was so convinced that Mr. Trump was psychologically unbalanced that he bought a book called “The Dangerous Case of Donald Trump,” written by 27 mental health professionals, to try to understand his boss better. As it was, Mr. Kelly came to refer to Mr. Trump’s White House as “Crazytown.”

Some of Mr. Trump’s cabinet secretaries had a running debate over whether the president was “crazy-crazy,” as one of them put it in an interview after leaving office, or merely someone who promoted “crazy ideas.” There were multiple conversations about whether the 25th Amendment disability clause should be invoked to remove him from office, although the idea never went far. His own estranged niece, Mary L. Trump, a clinical psychologist, wrote a book identifying disorders she believed he has. Mr. Trump bristled at such talk, insisting that he was “a very stable genius.”

“There were often discussions about whether he could comprehend or understand the policy and knowing that he didn’t really have a grasp on those kinds of things,” Ms. Matthews said of her time in the White House. “No one wanted to outright say it in that environment — is he mentally fit? — but I definitely had my moments where I personally questioned it.”

A 2022 study by a pair of University of Montana scholars found that Mr. Trump’s speech complexity was significantly lower than that of the average president over American history. (So was Mr. Biden’s.) The Times analysis found that Mr. Trump speaks at a fourth-grade level, lower than rivals like Gov. Ron DeSantis of Florida, who speaks at an eighth-grade level, which is roughly average for modern presidents.

Mr. Trump’s complexity level has remained relatively steady and has not diminished in recent years, according to the analysis. But concerns about his age have heightened now that he is trying to return to office, concerns that were not alleviated by his unfounded debate claim about immigrants “eating the pets” in a small town.

Polls show that a majority of Americans believe he is too old to be president, and his critics have been trying to focus attention on that. A group of mental health, national security and political experts held a conference at the National Press Club in Washington last month on Mr. Trump’s fitness. The Lincoln Project, an anti-Trump group of former Republicans, regularly taunts him with ads like one calling his debate with Ms. Harris “a cognitive test” that he failed.

Mr. Trump has appeared tired at times and has maintained a far less active campaign schedule this time around, holding only 61 rallies so far in 2024, compared with 283 through all of 2016, according to the Times analysis, although he has picked up the pace lately. He appeared to nod off during his hush-money trial in New York before being convicted of 34 felonies.

Experts said it was hard to judge whether the changes in Mr. Trump’s speaking style could indicate typical effects of age or some more significant condition. “That can change with normal aging,” said Dr. Bradford Dickerson, a neurologist at Harvard Medical School. “But if you see a change relative to a person’s base line in that type of speaking ability over the course of just a few years, I think it raises some real red flags.”

One person who has detected a change is Ramin Setoodeh, author of a new book on Mr. Trump’s days hosting “The Apprentice.” Mr. Setoodeh, who has written about Hollywood for years and first met Mr. Trump during his television days, was surprised at how much the former president had changed when he arrived at Mar-a-Lago for the first of six interviews for the book, “Apprentice in Wonderland.”

“The Donald Trump I interviewed in the early seasons of ‘The Apprentice’ had a stronger sense of time and space, and his narratives were a lot clearer,” Mr. Setoodeh said. “And the Donald Trump I interviewed for my book, ironically, could remember things that happened in the ‘Apprentice’ years well, but he struggled with more recent events.”

For instance, Mr. Trump could not remember the day in 2015 that NBC called to cut ties with him after he made derogatory remarks about Mexican immigrants. “He was very clear in terms of his memory of the shows,” Mr. Setoodeh said, even though his versions were often exaggerated or fabricated. “But when we went to more recent years, things got foggier.”

So foggy, in fact, that he forgot Mr. Setoodeh himself. After interviewing Mr. Trump in May 2021, Mr. Setoodeh returned in August. “When I said, ‘Do you remember sitting down with me?’ he said, ‘No, that was a long time ago,’” Mr. Setoodeh said. “It was like we started from square one. He started telling me the exact same stories. He didn’t remember what we had talked about. He didn’t remember me.”

Others who have encountered him since he left the White House have likewise described moments of forgetfulness. Most notable, perhaps, was his deposition in the defamation lawsuit brought by the writer E. Jean Carroll, who accused Mr. Trump of raping her in the 1990s. Shown a picture of Ms. Carroll, Mr. Trump confused her with his second wife, Marla Maples. (A jury later found that Mr. Trump sexually abused and defamed Ms. Carroll.)

Roberta Kaplan, who was Ms. Carroll’s lawyer, said Mr. Trump lost control at times during the proceedings, blowing up when he should have remained calm. “I assume that was always part of his personality,” she said in an interview. “But it may be getting worse.”

Others who have spent time with Mr. Trump in private, however, insist that they notice no difference.

“I never felt that cognitive ability or age was an issue,” said James Trusty, an attorney who represented Mr. Trump in his classified-documents criminal case until resigning last year after reported friction with another lawyer close to Mr. Trump.

“Like any high-powered executive, there were going to be times when he didn’t like hearing what I had to say or when we had spirited disagreements over strategy,” Mr. Trusty added. “But it was never something where I felt there was an intellectual disconnect.”

Sam Nunberg, a former Trump political adviser, said he still talked with people who see him almost daily, and had not heard of any concerns expressed about the former president’s age. “I don’t really see any major difference,” he said. “I just don’t see it.”

“He’s not linear,” he added. But “he was never linear.” At the debate with Ms. Harris, Mr. Nunberg said, Mr. Trump “seemed like he was tired” and “had an off night.” And, he added, “of course he doesn’t prepare.” But “that’s not like a Biden off night.”

Either way, watching recordings of Mr. Trump over the years yields a pretty clear evolution. The young media-obsessed developer and reality television star who spoke with a degree of sophistication and nuance eventually gave way to the bombastic presidential candidate with the shrunken vocabulary in 2016 and eventually to the aged former president seeking a comeback in 2024.

Consider the following: In 2002, Mr. Trump was interviewed for an Errol Morris documentary about “Citizen Kane,” the iconic Orson Welles film about a media tycoon. Mr. Trump gave a thoughtful analysis of the movie with a degree of introspection that would be hard to imagine today. “In real life, I believe that wealth does in fact isolate you from other people,” he said. “It’s a protective mechanism. You have your guard up much more so than you would if you didn’t have wealth.”

In 2011, as he was contemplating a run for the presidency, Mr. Trump addressed the Conservative Political Action Conference and sounded more partisan notes. While many of the themes would be familiar to today’s voters, he stuck closer to his script and finished his thoughts more often. His speeches in 2015 and 2016 were more aggressive, but still clearer and more comprehensible than now, and balanced with flashes of humor.

Now his rallies are powered as much by anger as anything else. His distortions and false claims have reached new levels. His adversaries are “lunatics” and “deranged” and “communists” and “fascists.” Never particularly restrained, he now lobs four-letter words and other profanities far more freely. The other day, he suggested unleashing the police to inflict “one really violent day” on criminals to deter crime.

He does not stick to a single train of thought for long. During one 10-minute stretch in Mosinee, Wis., last month, for instance, he ping-ponged from topic to topic: Ms. Harris’s record; the virtues of the merit system; Robert F. Kennedy Jr.’s endorsement; supposed corruption at the F.D.A., the C.D.C. and the W.H.O.; the Covid-19 pandemic; immigration; back to the W.H.O.; China; Mr. Biden’s age; Ms. Harris again; Mr. Biden again; chronic health problems and childhood diseases; back to Mr. Kennedy; the “Biden crime family”; the president’s State of the Union address; Franklin D. Roosevelt; the 25th Amendment; the “parasitic political class”; Election Day; back to immigration; Senator Tammy Baldwin; back to immigration; energy production; back to immigration; and Ms. Baldwin again.

Some of what he says is inexplicable except to those who listen to him regularly and understand the shorthand. And he throws out assertions without any apparent regard for whether they are true or not. Lately, he has claimed that crowds Ms. Harris has drawn were not real but the creation of artificial intelligence, never mind the reporters and cameras on hand to record them.

He mispronounces names and places with some regularity — “Charlottestown” instead of “Charlottesville,” “Minnianapolis” instead of “Minneapolis,” the website “Snoops” instead of “Snopes,” “Leon” Musk instead of “Elon.”

In Rome, Ga., he went on an extended riff about Mr. Biden in swim trunks on a beach. “Look, at 81 — do you remember Cary Grant? How good was Cary Grant, right? I don’t think Cary Grant, he was good. I don’t know what happened to movie stars today. We used to have Cary Grant and Clark Gable and all these people. Today we have — I won’t say names because I don’t need enemies. I don’t need enemies. I got enough enemies. But Cary Grant was like, Michael Jackson once told me, ‘The most handsome man, Trump, in the world.’ Who? ‘Cary Grant.’ Well, we don’t have that anymore. But Cary Grant at 81 or 82 — going on 100, this guy, he’s 81 going on 100 — Cary Grant wouldn’t look too good in a bathing suit either, and he was pretty good-looking, right?”

Talking on another occasion about how tough illegal immigrants are, he drifted off into a soliloquy about whether actors could portray them in a movie: “They can’t play the role. They’ll bring in a big actor and you look and you say, ‘Look, he’s got no muscle content. He’s got no muscle! We need a little muscle!’ Then they bring in another one. ‘But he’s got a weak face! He looks weak!’” Still, he has rather high regard for his own physique. “I could have been sunbathing on the beach,” he said at another point. “You have never seen a body so beautiful. Much better than Sleepy Joe.”

He considers himself the master of nearly every subject. He said Venezuelan gangs were armed “with MK-47s,” evidently meaning AK-47s, and then added, “I know that gun very well” because “I’ve become an expert on guns.” He claims to have been named “man of the year” in Michigan, although no such prize exists.

He is easily distracted. He halted in the middle of another extended monologue when he noticed a buzzing insect. “Oh, there’s a fly,” he said. “Oh. I wonder where the fly came from. See? Two years ago, I wouldn’t have had a fly up here. You’re changing rapidly. But we can’t take it any longer.”

But like some people approaching the end of their eighth decade, he is not open to correction. “Trump is never wrong,” he said recently in Wisconsin. “I am never, ever wrong.”