Some fundamental qualitative features of the dynamic response of chemical reacting systems to periodic forcing are described. Models considered are a homogeneous autocatalytic reaction (a Brusselator), a bimolecular surface reaction and the nonisothermal CSTR. These systems oscillate spontaneously, and the interaction of cycling an operating variable with the natural frequencies of the systems is examined. Numerical techniques employed include fixed point (shooting) as well as polynomial approximation methods for the computation of periodic trajectories, an algorithm for the computation of invariant tori and pseudo-arc length continuation of solution branches. Phenomena examined are entrainment, frequency locking, bifurcations to invariant tori, breaking of tori and period doubling cascades. Description of these phenomena in forced systems facilitates the understanding of coupling between nonlinear systems in general.