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In this paper, we present two efficient strategies for likelihood computation and decoding in a continuous speech recognizer using an underlying nonlinear state-space dynamic model for the hidden speech dynamics. The state-space model has been specially constructed so as to be suitable for the conversational or casual style of speech where phonetic reduction abounds. Two specific decoding algorithms, based on optimal state-sequence estimation for the nonlinear state-space model, are derived, implemented, and evaluated. They successfully overcome the exponential growth in the original search paths by using the path-merging approaches derived from Bayes' rule. We have tested and compared the two algorithms using the speech data from the Switchboard corpus, confirming their effectiveness. Conversational speech recognition experiments using the Switchboard corpus further demonstrated that the use of the new decoding strategies is capable of reducing the recognizer's word error rate compared with two baseline recognizers, including the HMM system and the nonlinear state-space model using the HMM-produced phonetic boundaries, under identical test conditions.