The frequency dependence of quadratic and cubic susceptibilities given by the conventional expressions for molecular crystals is analyzed for resonances (poles) in the light of the dielectric theory of excitons. Exciton frequencies correspond to poles in the local-held tensors; in the nonlinear susceptibilities the poles in these tensors cancel out the poles that occur in the hyperpolarizability where the output and input frequencies coincide with molecular excitation frequencies, and replace them by poles at the exciton frequencies, including wavevector dependence and any Davydov splitting. In the cubic susceptibility, there are additional poles, through cascading, where the sum of any two input frequencies coincides with an exciton frequency.