Abstract We analyze the onset of multiple oscillatory regimes in a two-variable biochemical model previously proposed for glycolytic oscillations. The model, based on the activation of an allosteric enzyme by a reaction product, is modified by introduction of recycling of product into the substrate. This modification creates the coiditions for birhythmicity in which two stable oscillatory regimes coexist under the same conditions. The detailed route by which birhythmicity develops from a single oscillatory regime is elucidated by means of bifurcation diagrams. It is shown that birhythmicity provides added sensitivity to the oscillatory system as the same type of perturbation may produce a switch from one periodic regime to the other and back, when applied at the appropriate phase of each of the two oscillations.