  In this paper we prove the persistence of hyperbolic invariant tori in
generalized Hamiltonian systems, which may admit a distinct number of action
and angle variables. The systems under consideration can be odd dimensional in
tangent direction. Our results generalize the well-known results of Graff and
Zehnder in standard Hamiltonians. In our case the unperturbed Hamiltonian
systems may be degenerate. We also consider the persistence problem of
hyperbolic tori on sub-manifolds.
