Continuous bioprocesses subject to time-invariant feed conditions are attractive due to ease of operation and control. Nonlinearities in kinetics of bioprocesses provide an opportunity to possibly improve the time-average performance of these by periodic forcing of feed conditions. This possibility is investigated in this article for cycling of dilution rate or feed concentration of the limiting substrate using the generalized pi-criterion. The analysis is facilitated by appropriate classification of continuous bioprocesses depending on the relations among the kinetics of cell growth, utilization of the limiting substrate, and synthesis of the desired non-biomass product. Very low-frequency periodic operations around the optimal steady state, if admissible, are proven to be non-optimal. Conditions for properness of periodic control and expressions for optimum cycling frequency are obtained analytically and frequency domains where periodic control is proper are identified. The pi-criterion is also employed to investigate if forced periodic operation may enable cell retention in continuous cultures under conditions where cell washout is the only admissible steady state. Multiplicity and stability characteristics of steady states are examined for few specific examples and portions of the operating parameter space where periodic operations involving weak variations in dilution rate or feed concentration of the limiting substrate are superior vis-a-vis continuous cultures operated at a stable non-trivial steady state are identified for each example.