MIAMI (Reuters) - American long-distance swimmer Diana Nyad pushed ahead on Monday, overcoming a night of lightning, rain and whipping winds in her latest bid to become the first person to swim from Cuba to Florida without a shark cage.

Nyad, who will turn 63 on Wednesday, was nearly a third of the way to Florida by Monday morning and swimming "strong," according to blog updates on her website (www.diananyad.com/blog).

The marathon swimmer battled adverse conditions on Sunday night after a squall "blew up very quick" and "all hell broke loose," the website said.

The storm spawned lightning and blew directly over her, briefly cutting off a GPS tracker that relayed data on her location and pushing Nyad east, it said.

"We had quite a night," her team said in a posted message. "The weather was really ugly."

As of 9:45 EDT (1345 GMT), Nyad was on course and stroking in calm waters. She has swum nearly 34 miles on her fourth attempt to make the 103-mile crossing through the shark-infested Florida Straits.

Nyad departed from the Cuban capital of Havana on Saturday afternoon accompanied by five boats and 50 crew members.

She is being protected in the warm waters by a special device that uses a mild electrical current to shield her from sharks.

Nyad was forced to abandon her last attempt last September to make the crossing after she was stung in the face and eyes by jellyfish. During this swim, she has a body suit that she will wear to protect against jellyfish stings, but does not plan on wearing it all the time.

Australian Susan Maroney successfully swam the Florida Straits in May 1997 at the age of 22 using a shark cage.

(Additional reporting by Jeff Franks in Havana; Writing by Kevin Gray; Editing by Will Dunham)