People in Florida are bracing themselves for Hurricane Wilma which is expected to strike on Monday morning.
The hurricane left Mexico's Gulf coast on Sunday after battering the Yucatan peninsula, killing at least six people.
In Cuba, there are high winds and heavy rains and several villages have been badly flooded by the storm.
After leaving Mexico, Wilma has strengthened to a category three storm - the strongest is a five - with winds of about 185km/h.
Florida Governor Jeb Bush had appealed on Sunday for people to leave the Florida Keys after it appeared many of its 80,000 residents had chosen to ignore the warnings.
"I cannot emphasise enough to the folks that live in the Florida Keys a hurricane is coming, and a hurricane is a hurricane and it has deadly force winds," he said.
Another tropical storm called Alpha has formed in the Caribbean, meaning 2005 is the busiest hurricane season on record.
It takes the number of storms named in the Atlantic to 22 this year.
Forecasters have used up all the names planned for storms this year and have now moved from the standard alphabet to the Greek alphabet - something they haven't done for almost 60 years.
The hurricane season still has five weeks left to run before it ends at the end of November.