The time-dependent anisotropy r(g)(t) - measured by exciting degenerate levels in an ensemble of stationary molecules of sufficiently high symmetry and probing a transition from the g-fold degenerate levels (g = 2 or 3) to a non-degenerate level - falls (within a few hundred femtoseconds) to an asymptotic value significantly lower than r(g)(0). The loss of electronic coherence in such systems is examined afresh. and the anisotropy is shown to follow a double or single exponential decay depending on whether the random variables of interest (population and phase) are statistically independent or not; some errors in previous derivations are also corrected. (C) 2002 Published by Elsevier Science B.V.