The process oi simultaneous utilization of two substitutable substrates for growth purposes in a continuously operated cyclic bioreactor was described with a mathematical model. The model assumes that all required nutrients except for the two substitutable resources are present in the reactor in excess at all times. Hence, the kinetics of the process depend only on the availability of the two substitutable substrates. Cyclic operation is imposed by the periodic harvesting of a fraction of the microbial suspension and replenishment of the harvested volume with an equal volume of fresh medium. The proposed model has been experimentally validated for its basic predictions by using a relatively simple system involving a pure culture of Pseudomonas putida (ATCC 17514) and media containing phenol and glucose as carbon and energy sources. The mathematical model was subjected to a detailed analysis of its dynamics through the use of computer algorithms based on the bifurcation theory for forced systems. II was found that self-substrate and cross-substrate inhibition terms which introduce nonlinearities in the denominator of the specific growth-rate expressions lead to regions of multistability in the operating parameter space. The effects of all five operating parameters, namely, concentration of the two substrates in the medium, dilution rate, fraction of reactor contents harvested, and fraction of cycle time devoted to replenishing the harvested suspension with fresh medium, on the dynamics of the system were investigated, and the results are presented in the form of two-dimensional projections of the operating diagram. Optimization studies were also performed and their results show that, in most cases, operating parameters can be selected in ways which maximize the working capacity of the reactor while achieving a desired conversion of at least one of the substrates.