The Nonhuman Rights Project filed writs of habeas corpus in an attempt to free the chimpanzees living in New York.
The suits demanded the animals, Tommy, Kiko, Hercules and Leo, be moved to one of the eight sanctuaries in the North American Primate Sanctuary Alliance.
The group told CNN it would appeal the decisions.
Pat Levery, Tommy's owner, said he was relieved the courts rejected the suits.
He said Tommy, who lives on a trailer lot in Gloversville, is well cared for, has many toys and a spacious cage.
Levery rescued Tommy from his previous home where he was badly treated.
The group said it plans to file more suits on behalf of other captive animals, include elephants, dolphins and whales.