Two Cuban boatpeople who escaped from a detention center in the Cayman Islands remained at large Tuesday and might have found a way to leave the Caribbean territory, officials said.

Authorities said Rafael Hidalgo Figueredo and Fernando Figueredo Corrales, both in their 30s, were reported missing Sunday, according to the Cayman News service.

One Cayman government official involved in the hunt for the Cubans said it was “not beyond the realm of the possible” that the pair might have been picked up by friends or relatives aboard a “go-fast” boat.

The two Cubans appeared to be part of a group of 17 who were detained in November after their wooden sailboat ran aground in shallow waters off one of the Cayman Islands.

They escaped from a government detention center in George Town, the main town in the British-run international banking and tourism center 125 miles from Cuba.

The Caymans are astride the route that Cuban boatpeople escaping from southern Cuba would take in hopes that the currents and winds would take them to Central America. They would then travel by land to the U.S. border.

At least five groups of Cubans fleeing their country were detained in the Cayman Islands in 2011, compared to none in 2010. The spike appeared to support reports indicating an increase in the number of Cubans trying to leave their island illegally in the past year.

Cayman policy until 2005 was that government officials and residents could help Cuban boatpeople spotted in territorial waters to continue their voyage by providing them with water, gasoline, food and boat repairs.

But now the Cubans are forced to go ashore as refuge seekers if their vessels are not considered to be seaworthy. If their boats are approved by Cayman authorities, they have the choice of continuing the trip or going ashore.

The Cubans who go ashore almost never apply for or receive refugee status, and are flown back to Cuba. Of the 1,200 who arrived during the so-called Rafter Crisis of 1994, only 20 won asylum.

The Cayman News Service reported that after the two Cubans escaped, police had warned “that it is a criminal offence to assist the Cubans who were picked up by the authorities.”