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 rare and feed concentration of the limiting substrate using the generalized pi-criterion. A unified analysis of optimality of forced periodic operation of continuous cultures producing a wide range of products and subject to periodic variation in either dilution rate or feed concentration of the limiting substrate has recently been reported (Parulekar, 1998, Chemical Engineering Science, 53, 2481-2502). The analysis is extended in this article, with the particular focus being the interaction effect due to simultaneous variations of the two input variables. Without placing any restrictions on the kinetics of the bioprocesses, it is established that subjecting a bioprocess to simultaneous periodic variations in dilution rate and substrate feed concentration does always lead to improved performance, at least at high frequencies. Where appropriate, analytical expressions are obtained for optimum phase difference (between periodic variations in the two inputs) and optimum amplitude ratio that lead to the maximum fractional improvement in the bioprocess performance (vis-a-vis operation at a steady state). Numerical illustrations pertain to bioprocesses generating many important metabolites. In each example, the two-dimensional control variable space is divided into appropriate regions based on differences in the effects of periodic variations in either or both inputs on the bioprocess. 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.