An approach to modeling nonlinear chemical kinetics using neural networks is introduced. It is found that neural networks based on a simple multivariate polynomial architecture are useful in approximating a wide variety of chemical kinetic systems. The accuracy and efficiency of these ridge polynomial networks (RPNs) are demonstrated by modeling the kinetics of H-2 bromination, formaldehyde oxidation, and H-2+O-2 combustion. RPN kinetic modeling has a broad range of applications, including kinetic parameter inversion, simulation of reactor dynamics, and atmospheric modeling. (C) 2004 American Institute of Physics.