The King-Altman-Hill graphic method has been widely used to derive the rate laws of enzymatic reactions, but the compilation of all the possible pathways is very time-consuming and the reaction rates are not given explicitly. In this study, the network reduction and Y-to-delta transformation techniques were systematically used to derive the general rate equations for pyramidal reaction networks in homogeneous catalysis. The enzymatic reaction of 7,8-dihydrofolate and NADPH to form 5,,6,6,8-tetrahydrofolate and NADP, catalyzed by dihydrofolate reductase was taken as an example to illustrate the application of the general reaction rate equations. The calculated overall reaction rate was compared with that obtained from the exact solution by matrix algebra and those obtained from the King-Altman-Hill graphic method. (C) 2003 Elsevier Science Ltd. All rights reserved.