When we periodically perturbed the central respiratory oscillator with a controlled periodic stimulation provided by a mechanical ventilator, an entrainment phenomenon occurred: the actual rhythm of the respiratory centres was phase locked to the periodic stimulation. In some experiments, we observed an intermittence phenomenon: the respiratory rhythm successively seemed entrained, departed from this mode for few cycles, returned to the previous pseudo entrainment and so on. From intermittence data, we were able to plot a phase response curve. From literature data on the effects of a single stimulation applied at various moments in the respiratory cycle, we built up a mathematical model designed to simulate entrainment experiments. This model simulated entrainment phenomenon, but did not satisfactorily accommodate the experimental phase response curve. The section of the simulated phase response curve responsible for discrepancies was the result of the combination of an inspiratory shortening owing to a stimulation occurring during inspiration, and a positive relationship between inspiratory duration TI and expiratory duration TE. We changed the TE-TI relationship, assuming that the expiratory duration is determined not by the inspiratory duration but rather by the lung volume at the end of inspiration. The revised model was then able to exhibit almost all the qualitative properties previously noted in experiments. The significance in biological terms of the new TE-TI relationship, which is apparently incompatible with almost all previous experimental data, is discussed.