A class of nonlinear control systems is considered whose state evolves in the neighborhood of a period orbit. Necessary and sufficient conditions are given for tracking a family of output reference trajectories while rejecting a family of disturbances both generated by a Poisson stable exosystem. A Poincare map approach is adopted to establish these conditions, along a path similar to the one recently proposed in the literature for a class of nonlinear control systems whose state evolves in the neighborhood of an equilibrium point. An illustrative example is included.