Autonomous oscillations in continuous microbial cultures can be modelled by periodic solution of the age distribution balance. When substrate or product concentrations in the medium affects passage through control points in the cell cycle, a positive feedback loop can form between the age distribution and the medium concentrations, and this may stabilize the oscillations and prevent a gradual loss of synchrony. An illustrative example is solved analytically and numerical simulations are used to determine the range of operating conditions over which oscillations may exist. Finally, autonomous oscillations in continuous cultures of Saccharomyces cerevisiae are discussed in the light of this model.