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Equations are developed which describe variable-volume cultivations, including fed-batch systems. An analogy is drawn between the quasi-steady state in variable-volume cultivation and a dynamic steady state in variable-flow, constant-volume chemostat bioreactors. Switching procedures are developed to give a steady-state transition from batch to fed-batch and to continuous operation. In this respect, considerations in the literature have been extended. Computer solutions of the governing differential equations verify the theory and provide insight into the behavior of variable-volume stirred tank reactors. Application of variable-volume cultivation as a tool in investigating growth rates at low substrate levels is suggested. Variable-volume bioreactor systems could be also to obtain controlled dynamic conditions for research or production purposes.