A nonlinear adaptive control strategy based on radial. basis function networks and principal component analysis is presented. The proposed method is well suited for low dimensional nonlinear systems that are difficult to model and control via conventional means. The effective system dimension is reduced by applying nonlinear principal component analysis to state variable data obtained from open-loop tests. This allows the radial basis functions to be placed in a lower dimensional space than the original state space. The total number of basis functions is specified a priori, and an algorithm which adjusts the location of the basis function centers to surround the current operating point is presented. The basis function weights are adapted on-line such that the plant output asymptotically tracks a linear reference model. A highly nonlinear polymerization reactor is used to compare the nonlinear adaptive controller to a linear state feedback controller that utilizes the same amount of plant information.