With the use of a molecular model for circadian rhythms in Drosophila based on transcriptional regulation, we show how a single, critical pulse of light can permanently suppress circadian rhythmicity, whereas a second light pulse can restore the abolished rhythm. The phenomena occur via the pulsatile induction of either protein degradation or gene expression in conditions in which a stable steady state coexists with stable circadian oscillations of the limit cycle type. The model indicates that suppression by a light pulse can only be accounted for by assuming that the biochemical effects of such a pulse much outlast its actual duration. We determine the characteristics of critical pulses suppressing the oscillations as a function of the phase at which the rhythm is perturbed. The model predicts how the amplitude and duration of the biochemical changes induced by critical pulses vary with this phase. The results provide a molecular, dynamic explanation for the long-term suppression of circadian rhythms observed in a variety of organisms in response to a single light pulse and for the subsequent restoration of the rhythms by a second light pulse.