Nyad, who turns 63 Wednesday, is making her third attempt since last summer to become the first person to swim across the Straits of Florida without a shark cage. She also made a failed try with a cage in 1978.
Nyad's team tweeted Monday morning that she was "swimming strong" in calm seas at 50 strokes per minute. She had covered almost 34 statute miles after leaving Havana on Saturday for the Florida Keys.
She's accompanied by a support team in boats. They tweeted Sunday night that a storm blew Nyad off course temporarily and that "all hell broke loose" in the squall. Nyad also suffered jellyfish stings.
Australian Susie Maroney successfully swam the Straits in 1997, but she used a cage. This June another Australian, Penny Palfrey, made it 79 miles toward Florida without a cage before strong currents forced her to abandon the attempt.
Nyad has already endured jellyfish stings on the current attempt. Stings forced her to cut short her second of two attempts last year as toxins built up in her system.
A kayak-borne apparatus shadowing Nyad helps keep sharks at bay by generating a faint electric field that is not noticeable to humans. A team of handlers is always on alert to dive in and distract any sharks that make it through.
Nyad has been training for three years and is in peak shape, according to friend and trainer Bonnie Stoll.
The team expects Nyad will take at least 60 hours to complete the swim, meaning she is scheduled to arrive in the Florida Keys sometime Tuesday.
She takes periodic short breaks to rest, hydrate and eat high-energy foods like peanut butter.