The authors acknowledge nancial support from DGYCIT (DGES PB98-1152), Junta de An-

We introduce and justify a computational scheme for the continuation of periodic orbits in systems with one or more rst integrals, and in particular in Hamiltonian systems having several independent symmetries. Our method is based on a generalization of the concept of a normal periodic orbit as introduced by Sepulchre and MacKay [21]. We illustrate the continuation method on some integrable Hamiltonian systems with two degrees of freedom and briefly discuss some further applications.