The mechanism of circadian oscillations in the period protein (PER) in Drosophila is investigated by means of a theoretical model. Taking into account recent experimental observations, the model for the circadian clock is based on multiple phosphorylation of PER and on the negative feedback exerted by PER on the transcription of the period (per) gene. This minimal biochemical model provides a molecular basis for circadian oscillations of the limit cycle type. During oscillations, the peak in per mRNA precedes by several hours the peak in total PER protein. The results support the view that multiple PER phosphorylation introduces times delays which strengthen the capability of negative feedback to produce oscillations. The analysis shows that the rhythm only occurs in a range bounded by two critical values of the maximum rate of PER degradation. A similar result is obtained with respect to the rate of PER transport into the nucleus. The results suggest a tentative explanation for the altered period of per mutants, in terms of variations in the rate of PER degradation.