Michael and Thelma King were found slain Friday at their condominium on the island of St. Martin, The Huffington Post reported.
The couple were condo owners in Mount Pleasant and have been described as being from South Carolina.
According to reports, their bodies were found "slashed."
A suspect was in custody as of Sunday, but he has not been charged.
Huffington Post reported:
Chief Prosecutor Hans Mos said both Americans appeared to have suffered fatal stab wounds. The woman was found tied to a chair, and the man was lying on the floor, partially over an overturned chair. Both were in their 50s.
Autopsies were expected to be conducted Monday, according to Mos. Relatives of the slain couple have arrived in the territory.