The effects of electronic coherence of doubly or triply degenerate levels are discussed, This coherence will show up in the anisotropy of a pump-probe experiment in which a pump pulse creates the coherence and a probe pulse connects the degenerate levels to a non-degenerate final state, Simple stochastic models for the decay of the anisotropy as a function of pump-probe delay are given, both for molecules with a high symmetry and for symmetric dimers and trimers, The possible role that degenerate level coherence may play in chemical reactions is also discussed, Finally, the stochastic models used to calculate the anisotropy decay are applied towards the calculation of absorption line shapes, Raman scattering and fluorescence.