The network reduction technique and the Bodenstein approximation of quasi-stationary behavior of reaction intermediates were systematically applied to derive general rate equations for reaction networks in homogeneous catalysis with and without inhibition. Single-cycle reaction networks with and without branches were considered. The general rate equations derived in this study are applicable for most enzymatic reactions and for some heterogeneous catalytic reactions involving first-order reactions with respect to the intermediates, but not applicable for the heterogeneous catalytic reactions involving bimolecular surface reaction, dissociative adsorption, or associative desorption. Examples of a simple reaction with inhibition were used to illustrate the application of the general rate equations for network elucidation.