A system of autonomous ordinary differential equations depending on a
small parameter is considered such that the unperturbed system has an
invariant manifold of periodic solutions that is not normally hyperbol
ic but is normally nondegenerate. The bifurcation function whose zeros
are the bifurcation points for families of perturbed periodic solutio
ns is determined. This result is applied to find the periodic solution
s near resonance for a two-degrees-of-freedom mechanical system modeli
ng a rotor interacting with an elastic support.