In 2010, Robert F. Kennedy Jr. was experiencing memory loss and mental fogginess so severe that a friend grew concerned he might have a brain tumor. Mr. Kennedy said he consulted several of the country’s top neurologists, many of whom had either treated or spoken to his uncle, Senator Edward M. Kennedy, before his death the previous year of brain cancer.

Several doctors noticed a dark spot on the younger Mr. Kennedy’s brain scans and concluded that he had a tumor, he said in a 2012 deposition reviewed by The New York Times. Mr. Kennedy was immediately scheduled for a procedure at Duke University Medical Center by the same surgeon who had operated on his uncle, he said.

While packing for the trip, he said, he received a call from a doctor at NewYork-Presbyterian Hospital who had a different opinion: Mr. Kennedy, he believed, had a dead parasite in his head.

The doctor believed that the abnormality seen on his scans “was caused by a worm that got into my brain and ate a portion of it and then died,” Mr. Kennedy said in the deposition.

Now an independent presidential candidate, the 70-year-old Mr. Kennedy has portrayed his athleticism and relative youth as an advantage over the two oldest people to ever seek the White House: President Biden, 81, and former President Donald J. Trump, 77. Mr. Kennedy has secured a place on the ballots in Utah, Michigan, Hawaii and, his campaign says, California and Delaware. His intensive efforts to gain access in more states could put him in a position to tip the election.

He has gone to lengths to appear hale, skiing with a professional snowboarder and with an Olympic gold medalist who called him a “ripper” as they raced down the mountain. A camera crew was at his side while he lifted weights, shirtless, at an outdoor gym in Venice Beach.

Still, over the years, he has faced serious health issues, some previously undisclosed, including the apparent parasite.

For decades, Mr. Kennedy suffered from atrial fibrillation, a common heartbeat abnormality that increases the risk of stroke or heart failure. He has been hospitalized at least four times for episodes, although in an interview with The Times this winter, he said he had not had an incident in more than a decade and believed the condition had disappeared.

About the same time he learned of the parasite, he said, he was also diagnosed with mercury poisoning, most likely from ingesting too much fish containing the dangerous heavy metal, which can cause serious neurological issues.

“I have cognitive problems, clearly,” he said in the 2012 deposition. “I have short-term memory loss, and I have longer-term memory loss that affects me.”

In the interview with The Times, he said he had recovered from the memory loss and fogginess and had no aftereffects from the parasite, which he said had not required treatment. Asked last week if any of Mr. Kennedy’s health issues could compromise his fitness for the presidency, Stefanie Spear, a spokeswoman for the Kennedy campaign, told The Times, “That is a hilarious suggestion, given the competition.”

The campaign declined to provide his medical records to The Times. Neither President Biden nor Mr. Trump has released medical records in this election cycle. However, the White House put out a six-page health summary for President Biden in February. Mr. Trump released a three-paragraph statement from his doctor in November.

Doctors who have treated parasitic infections and mercury poisoning said both conditions can sometimes permanently damage brain function, but patients also can have temporary symptoms and mount a full recovery.

Some of Mr. Kennedy’s health issues were revealed in the 2012 deposition, which he gave during divorce proceedings from his second wife, Mary Richardson Kennedy. At the time, Mr. Kennedy was arguing that his earning power had been diminished by his cognitive struggles.

Mr. Kennedy provided more details, including about the apparent parasite, in the phone interview with The Times, conducted when he was on the cusp of getting on his first state ballot. His campaign declined to answer follow-up questions.

In the days after the 2010 call from NewYork-Presbyterian, Mr. Kennedy said in the interview, he underwent a battery of tests. Scans over many weeks showed no change in the spot on his brain, he said.

Doctors ultimately concluded that the cyst they saw on scans contained the remains of a parasite. Mr. Kennedy said that he did not know the type of parasite or where he might have contracted it, though he suspected it might have been during a trip through South Asia.

Several infectious disease experts and neurosurgeons said in separate interviews with The Times that, based on what Mr. Kennedy described, they believed it was likely a pork tapeworm larva. The doctors have not treated Mr. Kennedy and were speaking generally.

Dr. Clinton White, a professor of infectious diseases at the University of Texas Medical Branch in Galveston, said microscopic tapeworm eggs are sticky and easily transferred from one person to another. Once hatched, the larvae can travel in the bloodstream, he said, “and end up in all kinds of tissues.”

Though it is impossible to know, he added that it is unlikely that a parasite would eat a part of the brain, as Mr. Kennedy described. Rather, Dr. White said, it survives on nutrients from the body. Unlike tapeworm larvae in the intestines, those in the brain remain relatively small, about a third of an inch.

Some tapeworm larvae can live in a human brain for years without causing problems. Others can wreak havoc, often when they start to die, which causes inflammation. The most common symptoms are seizures, headaches and dizziness.

There are roughly 2,000 hospitalizations for the condition, known as neurocysticercosis, each year in the United States, according to the journal Emerging Infectious Diseases.

Scott Gardner, curator of the Manter Laboratory for Parasitology at the University of Nebraska-Lincoln, said that once any worm is in a brain, cells calcify around it. “And you’re going to basically have almost like a tumor that’s there forever. It’s not going to go anywhere.”

Dr. Gardner said it was possible a worm would cause memory loss. However, severe memory loss is more often associated with another health scare Mr. Kennedy said he had at the time: mercury poisoning.

Mr. Kennedy said he was then subsisting on a diet heavy on predatory fish, notably tuna and perch, both known to have elevated mercury levels. In the interview with The Times, he said that he had experienced “severe brain fog” and had trouble retrieving words. Mr. Kennedy, an environmental lawyer who has railed against the dangers of mercury contamination in fish from coal-fired power plants, had his blood tested.

He said the tests showed his mercury levels were 10 times what the Environmental Protection Agency considers safe.

At the time, Mr. Kennedy also was a few years into his crusade against thimerosal, a mercury-containing preservative used in some vaccines. He is a longtime vaccine skeptic who has falsely linked childhood inoculations to a rise in autism, as well as to other medical conditions.

In the interview, Mr. Kennedy said he was certain his diet had caused the poisoning. “I loved tuna fish sandwiches. I ate them all the time,” he said.

The Times described Mr. Kennedy’s symptoms to Elsie Sunderland, an environmental chemist at Harvard who has not spoken to Mr. Kennedy and responded generally about the condition.

She said the mercury levels that Mr. Kennedy described were high, but not surprising for someone consuming that quantity and type of seafood.

Mr. Kennedy said he made changes after these two health scares, including getting more sleep, traveling less and reducing his fish intake.

He also underwent chelation therapy, a treatment that binds to metals in the body so they can be expelled. It is generally given to people contaminated by metals, such as lead and zinc, in industrial accidents. Dr. Sunderland said that when mercury poisoning is clearly diet-related, she would simply recommend that the person stop eating fish. But another doctor who spoke to The Times said she would advise chelation therapy for the levels Mr. Kennedy said he had.

Mr. Kennedy’s heart issue began in college, he said, when it started beating out of sync.

In 2001 he was admitted to a hospital in Seattle while in town to give a speech, according to news reports. He was treated, and released the next day. He was hospitalized at least three additional times between September 2011 and early 2012, including once in Los Angeles, he said in the deposition. On that visit, he said, doctors used a defibrillator to shock his heart to reset the rhythm.

He said in the deposition that stress, caffeine and a lack of sleep triggered the condition. “It feels like there’s a bag of worms in my chest. I can feel immediately when it goes out,” he said.

He also said in the deposition and the interview that he had contracted hepatitis C through intravenous drug use in his youth. He said he had been treated and had no lingering effects from the infection.

Mr. Kennedy has spoken publicly about one other major health condition — spasmodic dysphonia, a neurological disorder that causes his vocal cords to squeeze too close together and explains his hoarse, sometimes strained voice.

He first noticed it when he was 42 years old, he said in the deposition. Mr. Kennedy for years made a significant amount of money giving speeches, and that business fell off as the condition worsened, he said.

He told an interviewer last year that he had recently undergone a procedure available in Japan to implant titanium between his vocal cords to keep them from involuntarily constricting.