As of 6:45 p.m. EDT, she had been in the water 33 hours and 45 minutes, a post on her website's blog said.
Blogger Bonnie Stoll said Nyad "is feeling strong and very coherent."
"She is joking for the first time all day," Stoll said.
"The only concern is that she is throwing up everything she eats. She's quite nauseous from sea salt, but that's to be expected. It's very normal for her and we've seen it in any of her swims over 15 hours or so.
"We're just going to keep feeding her and we hope that some of it is going down. She's not weak. Her stroke count hasn't changed."
CNN reported Nyad had traveled more than 63 miles by the time she had reached the 30-hour mark.
"This is farther than she has gone in any previous attempt," team navigator John Bartlett wrote on Nyad's website, noting she was being aided by a favorable current.
An earlier post on the website said she was maintaining her pace of 47 strokes a minute, CNN said. She began her swim Saturday morning in Havana. The journey is expected to take about three days.
Nyad is making her fifth attempt to swim from Cuba and Florida without benefit of a shark cage, flippers or wet suit, something no one has ever done. She has said if she doesn't make it this time, she won't try again, CNN said.