Sustained oscillations have been observed in continuous cultures of Saccharomyces cerevisiae. These oscillations appear spontaneously under aerobic conditions and may constitute a severe limitation for process control. We have found that oscillations arise only in a well defined range of dilution rates and dissolved oxygen values. The period of the oscillations is related, but not equal, to the mass doubling time, and shows a relation ship with both the parent cells and daughter cells generation times. At high dilution rates two oscillatory regimens, with different periods, are observed. The analysis of the budding index shows a marked degree of synchronization of the culture, however significant differences, both in phase and in amplitude, are ob served if the budding index of parent cells and of daughter cells are considered separately. The complex changes of the cell population are clearly demonstrated by the continuous and periodic modification of both cell volume distributions and protein distributions. Ethanol is always accumulated before the drop of dissolved oxygen concentration and one of the peaks of budding index. We propose a model that explains the insurgence of these oscillation as a consequence of changes in cell cycle parameters due to alternate growth in glucose and in ethanol.