In this paper we propose a novel order-recursive training algorithm for kernel-based discriminants which is computationally efficient. We integrate this method in a hybrid HMM-based speech recognition system by translating the outputs of the kernel-based classifier into class-conditional probabilities and using them instead of Gaussian mixtures as production probabilities of a HMM-based decoder for speech recognition. The performance of the described hybrid structure is demonstrated on the DARPA Resource Management (RM1) corpus.