Potential improvement in performance of continuous processes via weak periodic perturbations in one or more process inputs is systematically analyzed using the generalized pi-criterion. At very low forcing frequencies, the performance of a periodically forced continuous process is tied to the second total differentials of the objective function at steady state. Periodic forcing of multiple inputs and the role of binary interactions between multiple inputs are analyzed in detail. Where permissible, conditions for properness of periodic control are derived and expressions for optimum phase differences (between input pairs), optimum amplitude ratios, and the maximum performance improvement vis-a-vis steady state operation are obtained. The powerful analytical results are applicable for any continuous process. Two illustrations, one dealing with antibiotic selection in recombinant cell cultures and the other dealing with series-parallel reactions, are considered for numerical study. Portions of the operating parameter space (base values of input variables and forcing frequency) where periodic operations involving weak variations in one or more inputs are superior to optimal steady state operation are identified for each illustration. An increase in the number of inputs perturbed is demonstrated to lead to broadening of the regions in the operating parameter space where forced periodic operations are superior to steady state operation and also to improved process performance. Both analytical and numerical results reveal the significant benefits of binary input interactions. (C) 2003 Elsevier Ltd. All rights reserved.