Nyad jumped into the water near Havana Sunday night. The 61-year-old is about one-third of the way into what she expects to be a two-and-a-half day swim to the Florida coast.
She is trying to set a record as the first person to make the 103-mile swim without a shark cage, relying instead on an electrical field from equipment towed by kayakers to keep them at bay.
She's taking short pauses for nourishment and is not allowed to touch the support boat. On her Facebook page her support crew says they are very pleased with her progress.
Nyad attempted the same swim at 28 years old unsuccessfully due to weather and water conditions. If completed, she would break her own record of 102.5 miles for a cageless, open-sea swim, set in 1979 when she stroked from the Bahamas to Florida.
A post to Nyad's Twitter account suggests she's determined to go all the way.
"If I go unconscious, that's one thing," it read. "But no one is going to make me get out of the water, that will never happen."
Nyad told journalists she hopes her swim will inspire others her age to live active lives. She also hopes it can help improve understanding between Cold War rivals Cuba and the United States, even if just symbolically.
The Associated Press contributed to this story.