In this study we examine the operation of a continuous biochemical reactor in which cell reproduction is by mitosis. The uniqueness of steady-state operating points and the stability of these points are investigated. The system operated with a biomass-clear feed, a biomass-laden feed, and sinusoidally varying feed and effluent flow rates is analyzed. These modes of operation are suggested by commercial operation of sewage treatment facilities, as well as other continuous biochemical systems. Of these different ways of operating the reactor a biomass-laden feed and steady flow rates are required for a unique steady state operating point to exist. In all cases the system stability is governed by the nature of the specific death function describing the age-dependent probability of mitosis occurring.