(Updates with storm becoming hurricane, position, details)

MIAMI, Nov 6 (Reuters) - Tropical Storm Paloma grew into a Category 1 hurricane on Thursday and was expected to strengthen further as it churned through the Caribbean on a path that threatens the Cayman Islands and storm-weary Cuba, U.S. forecasters said.

The 16th storm of the 2008 Atlantic hurricane season posed no threat to vital U.S. oil installations in the Gulf of Mexico.

But it came in the last month of what experts correctly predicted would be a busier than normal storm season and may bring more grief to Cuba, which is still reeling from two powerful hurricanes that caused more than $5 billion in damage two months ago.

At 7 p.m. EST (0000 GMT), Paloma was located 165 miles (265 km) south of Grand Cayman Island and was moving to the north at about 12 miles per hour (19 km per hour), the U.S. National Hurricane Center said.

Its sustained winds had grown to 75 mph (120 kph), making it a Category 1 hurricane on the five-step Saffir-Simpson intensity scale, the Miami-based hurricane center said.

"Paloma continues to rapidly organize and additional strengthening is likely," the hurricane center said in a statement. Forecasters expected it to be a Category 2 hurricane before it hits Cuba on Sunday.

Paloma dumped rain on Honduras and Nicaragua on Thursday.

"In the higher areas of Gracias a Dios the rains have started and we expect flooding. We are telling people in the area to leave the mountain areas, there are a lot of people at risk," said Randolfo Funes, an official at Honduras' rescue agency Copeco.

A hurricane warning was in effect for the Cayman Islands meaning that hurricane conditions, including rainfall totaling up to 12 inches (30 cm) over parts of the wealthy British territory, were possible within 24 hours.

Jamaica could also be affected as the storm churns north and then makes an expected turn to the northeast.

Computer models varied on the future intensity of the storm. But the hurricane center's official forecast called for it to become a Category 2 hurricane with top winds of 104 mph (167 kph), U.S. forecasters said, adding that it was likely to plow across central Cuba on Sunday before weakening back into a tropical storm as it takes aim at the Bahamas.

Paloma became the 8th hurricane of the Atlantic storm season, which runs from June 1 to Nov. 30. (Additional reporting by Gustavo Palencia in Tegucigalpa) (Reporting by Jim Loney, editing by Philip Barbara)

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