A high performance speaker-independent isolated-word hybrid speech recognizer was developed which combines Hidden Markov Models (HMMs) and Radial Basis Function (RBF) neural networks. In recognition experiments using a speaker-independent E-set database, the hybrid recognizer had an error rate of 11.5% compared to 15.7% for the robust unimodal Gaussian HMM recognizer upon which the hybrid system was based. These results and additional experiments demonstrate that RBF networks can be successfully incorporated in hybrid recognizers and suggest that they may be capable of good performance with fewer parameters than required by Gaussian mixture classifiers. A global parameter optimization method designed to minimize the overall word error rather than the frame recognition error failed to reduce the error rate.