A U.S. couple accused of kidnapping their two sons in Florida and fleeing to Cuba by boat were turned over to U.S. authorities, who arrested the man and the woman, authorities in Florida's Hillsborough County announced Wednesday.

The parents of the two young boys remain under arrest and are waiting to appear in court so that charges can be presented against them, a spokesman with the Hillsborough County Sheriff's Office told Efe.

The parents - Joshua Michael Hakken, 36, and his wife, Sharyn Patricia Hakken, 35 - as well as their two sons, 3-year-old Chase Julian and 5-year-old Cole Travis, whose maternal grandmother had custody of them, were turned over by Cuba to the United States after the parents sailed to the island.

The children were taken from the home of their maternal grandmother by Joshua Hakken, although his wife also participated in the abduction.

The parents later used a 7.5-meter (about 24 feet) boat, the Salty Paw, to flee with the boys to Cuba, where they docked at the Hemingway Marina, in Havana.

Upon learning of the double kidnapping, Louisiana authorities made public details about the parents and the reasons why custody of the boys had been turned over to the grandmother.

Louisiana officials said that in June 2012 police responded to a complaint that the couple was making too much racket in a Louisiana hotel room, where the children were and where later drugs and weapons were found.

Joshua Hakken was arrested and Louisiana authorities temporarily took custody of the boys, but after a time, officials decided to give their maternal grandmother, a Florida resident, permanent custody.

Cuban authorities informed the U.S. Interests Section in Havana last Monday, and later the U.S. State Department in Washington, that the family was in Cuba. EFE