Summary: In this paper, we describe a new approach to speech enhancement by modeling directly the statistical characteristics of the speech waveform. To represent the nonlinear and nonstationary nature of speech, it is assumed that speech is the output of a neural predictive hidden Markov model (NPHMM). The NPHMM is a nonlinear autoregressive process whose time-varying parameters are controlled by a Markov chain. Given some speech data, the parameter of NPHMM is estimated by a learning algorithm based on the combination of Baum–Welch algorithm and a neural network learning algorithm using the well-known back propagation technique. Given the parameters of NPHMM, a recursive estimation method using multiple Kalman filters, governed by a Markov state chain according to the transition probabilities is developed for enhancing speech signals degraded by statistically independent additive noise characteristics assumed to be white and Gaussian. Under various input signal-to-noise ratios (SNRs), the proposed recursive speech enhancement method achieves an improvement over the method based on hidden filter model of about 0.8-1.2 dB in terms of the measured output SNR.