Nyad, who turns 63 Wednesday, reached the 50-hour mark of her swim about 5:30 p.m. EDT.
At 3:24 p.m. EDT, when Nyad had been in the water for 47 hours and 41 minutes, she was about 75 miles from Key West, a post on her Web site said.
A storm and an encounter with jellyfish Sunday night greatly hampered her progress, her Web site said.
Dr. Angel Yanagihara said Monday afternoon Nyad was "doing very well" and was "swimming strong."
Yanagihara said Sunday night had been a complete nightmare" with Nyad coming in contact with a box jellyfish.
"We had to pull a piece of tentacle off her fingers," she said. "We responded with some treatments that I have developed at the University of Hawaii at my research lab, and [she] reacted well to the treatment. She got some confidence back and reduced her pain. She went back out, just soldiering on."
Yanagihara said the treatment routine was repeated several times during the night.
"It was really exhausting just for us on the boat, but she kept going strong through all that," she said.
Brandon Beach, captain of Nyad's support boat, said the weather was calm through the day Monday, with about 1 foot waves, single-digit winds from the southeast and clear skies.
Nyad began her attempt to swim the 103 miles from Cuba to Florida without the protection of a shark cage Saturday.
Her try last year ended after 41 hours in the water after she was stung by jellyfish.
The noted long-distance swimmer once swam around the island of Manhattan (1975) and 102 miles from the Bahamas to Florida (1979).