Theoretical models considering inhomogeneous energy splitting effects are developed to explain impulsive pump-probe polarization anisotropy experiments on degenerate states of square symmetric molecules and chromophore pairs with perpendicular transition dipoles. When detecting the pump-induced change in probe transmission through the sample, the pump-probe signal arises from lost absorption due to ground state depopulation, stimulated emission from the singly excited states, and absorption from the singly excited states to doubly excited states. Including coherence between the singly excited states, the total impulsive initial anisotropy is 2/5 in all cases. In contrast to the first and second contributions, the time dependent excited state absorption anisotropy depends on a cyclic set of four transition dipoles, not just the energetic splitting. Ignoring molecular rotation, inhomogeneous anisotropy dynamics arise only for coupled chromophore pairs and Jahn-Teller distortions of the degenerate state that produce a cyclic set of transition dipoles different from the set for uncoupled direct product states. In all systems treated, a time dependent pump-probe anisotropy requires coupling between excitations. (C) 2003 American Institute of Physics.