Multiphoton spectroscopy is increasingly being used for the study of molecular excited states. The increase in the transition rate under resonance conditions can be exploited as a means of locating new states, and the dependence of the rate on the photon polarizations gives information about state symmetries. In this paper, expressions for the rate of doubly resonant three-photon absorption are derived, and it is shown how these results can be applied to various other stimulated processes. It is also demonstrated how the relative orientations of molecular transition moments can be found by performing a specified set of experiments with different polarizations. In addition to providing symmetry information, this method may prove a valuable means of testing molecular wave function calculations for biological molecules.