We propose a molecular model for InsP3-sensitive Ca2+ oscillations based on the allosteric properties of the InsP3 receptor/Ca2+ channel. Our model interprets the cooperatively towards InsP3 saturation, of calcium efflux from intravesicular stores as well as the absence of cooperativity in the binding process of InsP3 on the receptor. It takes into account quantitatively the two antagonist, concentration-dependent effects (fast activator and slow inhibitor) that cytosolic Ca2+ exerts on the InsP3 receptor/Ca2+ channel. Assuming that a single pool of releasable Ca2+ exists in the endoplasmic reticulum, the model leads to cytosolic and intravesicular oscillations in Ca2+ at fixed InsP3 concentration. Activation of the receptor by cytosolic calcium is essential for the triggering of oscillations whereas the slow Ca2+ inhibition effect is irrelevant in this respect, although this regulation loop might prevent the system from entering the unstable domain in absence of a true agonist stimulation. Activating cytosolic Ca2+ and InsP3 have quite distinct functions for the induction of Ca2+ release: cytosolic Ca2+ triggers oscillations whereas InsP3 only brings the receptor into a potentially oscillatory regime. Hence, the increasing slope of Ca2+ spiking is constitutively independent from the intensity of the hormonal stimuli in our model, in accord with experimental observations. Comparisons with other existing models are given and additional possible coupling mechanisms are discussed in order to explain particular facts (such as possible oscillations of InsP3) which do not depend on the intrinsic properties of the oscillator.