Hurricane Gustav, which has reached a fearsome Category 4, has roared through western Cuba en route to the US.
The storm hit Cuba's western Pinar del Rio province on Saturday with winds of up to 240km/h (150mph), causing damage to property but no reported fatalities.
More than 300,000 people had been evacuated from coastal areas in Cuba, to escape extensive flooding.
The storm had earlier killed more than 80 people when it swept through the Caribbean.
Four people were killed in Jamaica, where the storm also shattered roads and bridges such as this one in Kingston.
The Caymans felt its force on Friday night, with storm surges and heavy rain flooding. People took refuge in government shelters and there were no reports of injuries.
The storm is predicted to reach America's north Gulf Coast on Monday and local people have been securing their property as best they can.
The mayor of New Orleans has issued a mandatory evacuation order and warned that anyone deciding to stay behind would be making "the biggest mistake of their lives".
The order covers every person in the city, including the emergency services - only a handful of city workers will remain behind.
Thousands of New Orleans residents have been leaving the city by car, fearing a repeat of the Hurricane Katrina disaster of 2005.