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Based on the SS-model [Somogyi R and Stucki J W J. Biol. Chem. 266 (1991) 11 068] for the generation of intracellular Ca2+ concentration oscillations, we consider a time delay for the binding kinetics of the Ca2+ channel and find a significant phenomenon that the oscillation takes two quite different modes when a parameter of the system crosses a threshold. One is a quick oscillation mode and the other is a slow oscillation mode. The oscillation frequencies of these modes differ from each other by more than ten times. The change of oscillation form with parameters and its critical behaviour are illustrated by numerical simulation results.