  In this article we prove two versions of the Liapunov center theorem for
symmetric potentials. We consider a~second order autonomous system $\ddot
q(t)=-\nabla U(q(t))$ in the presence of symmetries of a compact Lie group
$\Gamma$ acting linearly on $\mathbb{R}^n.$ We look for non-stationary periodic
solutions of this system in a~neighborhood of an orbit of critical points of
the potential $U.$
