A comment post to a Cayman News story reported that a third boat had been spotted, El Nuevo Herald in Miami reported Monday. There was no confirmation from officials.
The first boat with 32 passengers was sighted off Cayman Brac on Friday, El Nuevo Herald said. Police reports said some on the boat were treated for seasickness and the group was then allowed to resume the voyage.
The second with 13 men and two women on board was spotted Saturday in the waters of Boden Town on Grand Cayman.
The Caymans are a British overseas territory. Most Cubans who seek asylum there are returned to Cuba.
In 1994, about 1,400 Cubans reached the Caymans, but only 20 were allowed to remain.
The islands lie southeast of Cuba and refugees trying to reach Honduras frequently cross Cayman territorial waters. Honduras is a popular destination for Cubans hoping to enter the United States via Mexico.
While most of the comments on the Cayman News story appeared to support the government's policy, some noted that the Caymans welcome rich tourists and people wishing to take advantage of the country's financial services.
"We dont have 'any room in the inn' but we do have a tiny room in our 'manger' which is currently being shared between five Filipinos and three Indians," a reader using the name Knot S Smart wrote.