In an effort to advance the state of the art in continuous speech recognition employing hidden Markov models (HMM), Segmental Neural Nets (SNN) were introduced recently to ameliorate the wellknown limitations of HMMs, namely, the conditional-independence limitation and the relative difficulty with which HMMs can handle segmental features. We describe a hybrid SNN/I-IMM system that combines the speed and performance of our HMM system with the segmental modeling capabilities of SNNs. The integration of the two acoustic modeling techniques is achieved successfully via the N-best rescoring paradigm. The N-best lists are used not only for recognition, but also during training. This discriminative training using N-best is demonstrated to improve performance. When tested on the DARPA Resource Management speaker-independent corpus, the hybrid SNN/HMM system decreases the error by about 20% compared to the state-of-the-art HMM system