Role of Ca2+ oscillations at fertilization in mammals: In all mammalian species, sperm-egg fusion leads to repetitive increases in the level of cytosolic Ca2+. These oscillations play an important role in the relief of the egg from its arrested state. To undestand the mechanism by wich egg development could be optimized by an appropriate pattern of Ca2+ oscillations, the interactions between the cell cycle and the intracellular Ca2+ dynamics have to be investigated. On the basis of the available experimental datas, a model involving the well-known activation of calmodulin-dependent kinase II by Ca2+ has been developed. To account for experimental observations, it has to be assumed that CaMKII interferes with the cell cycle oscillator at two distinct levels, the 2 pathways being characterized by different kinetics. The model thus accounts for the observed dependence of the time of entry in interphase on the frequency of the Ca2+ spikes, as well as for the possible entry in metaphase III, a pathological state of the egg which results from an insufficient activation by Ca2+. Possible mechanism for bursting-type complex Ca2+ oscillations: In most cases, Ca2+ oscillations appear as periodic increases of the level of cytosolic Ca2+ from the basal level up to a high concentration of the order of 1 µM. In response to specific agonists, some cells as hepatocytes display oscillations of the bursting type, i.e. a large-amplitude Ca2+ spike followed by small-amplitude variations around a plateau-level. The possible mechanisms of such complex oscillations have been investigated. Amoung various possibilities, a model based on the interplay between Ca2+-induced Ca2+ release and the Ca2+-activated metabolism of InsP3 by 3-kinase displays interesting properties. In particular, it can explain the experimental observation that Ca2+ oscillations are very little affected by the overexpression of InsP3 3-kinase, one of the two enzymes responsible for InsP3 degradation.