  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.
