  In this paper, we show how to use canonical perturbation theory for
dissipative dynamical systems capable of showing limit cycle oscillations.
Thus, our work surmounts the hitherto perceived barrier for canonical
perturbation theory that it can be applied only to a class of conservative
systems, viz.,~Hamiltonian systems. In the process, we also find Hamiltonian
structure for an important subset of Li\'enard system--- a paradigmatic system
for modeling isolated and asymptotic oscillatory state. We discuss the
possibility of extending our method to encompass even wider range of
non-conservative systems.
