Experimental observations have put in evidence autonomous self-sustained cir-cadian oscillators in most mammalian cells, and proved the existence of molecular links between the circadian clock and the cell cycle. Some mathematical models have also been built to assess conditions of control of the cell cycle by the circadian clock. However, recent studies in individual NIH3T3 fibroblasts have shown an unexpected acceleration of the circadian clock together with the cell cycle when the milieu is enriched in FBS, the absence of such acceleration in confluent cells, and the absence of any period doubling phenomena. In order to explain these observations, we study a possible entrainment of the circadian clock by the cell cycle through a regulation of clock genes around the mitosis phase. We develop a computational model and a formal specification of the observed behavior to investigate the conditions of entrainment in period and phase. We show that either the selective inhibition of Bmal1 transcription, or the selective activation of RevErb-α at the end of the mitosis phase, allow us to fit the experimental data, while a uniform inhibition of transcription during mitosis seems incompatible with the phase data. We conclude on some further $ This article is the extended revision of a preliminary communication published in [1]. Email addresses: Pauline.Traynard@inria.fr (Pauline Traynard), Celine.Feillet@unice.fr (Céline Feillet), Sylvain.Soliman@inria.fr (Sylvain Soliman), Franck.Delaunay@unice.fr (Franck Delaunay), Francois.Fages@inria.fr (François Fages) Preprint submitted to Elsevier December 19, 2015 predictions of the model.