A first-harmonic balance approach is proposed for fast evaluation of the dynamics of nonlinear periodically operated chemical reacting systems. The approach is based on approximating nonlinearities by means of the first-harmonic Fourier series and carries 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. Two systems involving nth-order heterogeneous catalytic reaction and diffusion transport were 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 gains in reactant conversion depend on the reaction order, and on the amplitude and the frequency of the forcing signal. In the case of diffusion transport, important flux improvements are obtained for relatively low values of the forcing frequency. (C) 2012 Elsevier Ltd. All rights reserved.