Résumé : Experimental observations performed in the p53-Mdm2 network, one of the key protein module involved in the control of proliferation of abnormal cells in mammals, revealed the existence of two frequencies of oscillations of p53 and Mdm2 in irradiated cells depending on the irradiation dose. Recently, Ouattara, Abou-Jaoudé and Kaufman proposed a 3-dimensional differential model showing birhythmicity, i.e. the coexistence between two stable oscillatory regimes for the same external conditions, to reproduce the two frequencies experimentally observed. Here we analyze the mechanisms at the origin of the birhythmic behaviour through a theoretical exploration of this differential model. Our approach is to approximate this 3-dimensional continuous non-linear model which is difficult to analyse into a 3-dimensional then 2-dimensional piecewise affine model. A first return map analysis can then be used to extract the basic mechanisms for the emergence of birhythmicity. Based on this analysis, an experimental strategy is proposed to test the existence of birhythmicity in the p53-Mdm2 network.