  This paper is devoted to the study of periodic solutions of Hamiltonian
system $\dot z(t)=J \nabla H(z(t))$, where $H$ is symmetric under an action of
a compact Lie group. We are looking for periodic solutions in a nearby of
non-isolated critical points of $H$ which form orbits of the group action. We
prove Lyapunov-type theorem for symmetric Hamiltonian systems.
