A first-harmonic balance approach is proposed to analyze the time-average performance of nonlinear periodically operated continuous bioreactors. The approach is based on approximating nonlinearities by means of the first-harmonic Fourier series and carry out a first-harmonic balance of the system dynamics. The application of this procedure leads to a set of nonlinear equations that are numerically solved to obtain the time-average parameters of the system response. Simple variants of the Monod function are used to illustrate the application and accuracy of the first-harmonic balance methods. The numerical results showed the ability of the proposed approach to give a simple and accurate description of the effects introduced by periodic operation. It is shown that, for the case investigated, the gain in biomass production as compared to the unforced case, depends on the yield function as well as on the amplitude and the frequency of the forcing signal. (C) 2011 Elsevier B.V. All rights reserved.