The move would allow the animals to be released into sanctuaries where they could live out the reminder of their days in freedom, says the Nonhuman Rights Project behind the initiative.
On Monday it petitioned a court in Fulton County Court, New York State, in the name of Tommy, a chimpanzee held captive in a cage at a used trailer lot in nearby Gloversville.
Yesterday it did the same for Kiko, a 26-year-old chimpanzee who is deaf and living in a private home in Niagara Falls.
"The lawsuits ask the judge to grant the chimpanzees the right to bodily liberty and to order that they be moved to a sanctuary," the organisation said in a statement.
There the animals can live out their days in an environment as close to the wild as is possible in North America, it added.
The challenge is based on the principle of habeas corpus, which the petitioners said was used in New York and allowed slaves to challenge their status and establish their right to freedom.
The courts can decide whether or not to take up the petitions but if they refuse the organisation has the right of appeal.
The Nonhuman Rights Project works to change the common law status of at least some animals to "persons" who possess fundamental rights such as bodily integrity and bodily liberty.
