Existence of relative periodic orbits near relative equilibria

We show existence of relative periodic orbits (a.k.a. relative nonlinear normal modes) near relative equilibria of a symmetric Hamiltonian system under an appropriate assumption on the Hessian of the Hamiltonian. This gives a relative version of the Moser-Weinstein theorem. The paper supersedes an earlier paper (this arxiv math.SG/9906007), which contains a mistake.