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Perrin's elliptical oscillator model for the anisotropy of optical properties due to degenerate transitions in planar molecules is extended to include time dependence. It is found necessary to revise the physical model so that it consists of two perpendicular Lorentz oscillators having mutual phase and population relaxation. The predictions of the revised model are consistent with but not identical to those obtained from a density matrix approach and provide unique specifications of the rates of population exchange and dephasing.