In the wild, the sugar glider's main predators are large predatory birds such as owls and hawks. Sugar gliders should not be kept in the same room as parrots and other screeching birds because gliders are stressed by their calls.
 
Don’t let your cat or dog close to your sugar glider’s cage because their presence can stress your glider. Don’t allow cats, dogs or ferrets to interact with a sugar glider. These animals are predators and can kill your sugar glider.

Sugar gliders can harm mammals smaller than themselves such as baby mice or hamsters, so keep gliders away from these smaller pets.