This paper describes new modeling methods combining neural network and hidden Markov model applicable to modeling a time series such as speech signal. The idea assumes that the sequence is nonstationary and is a nonlinear autoregressive process whose parameters are controlled by a hidden Markov chain. One is the model where a non-linear predictor composed of a multi-layered neural network is defined at each state, another is the model where a multi-layered neural network is defined so that the path from the input layer to the output layer is divided into path-groups each of which corresponds to the state of the Markov chain. The latter is an extended model of the former. The parameter estimation methods for these models are shown, and other previously proposed models--one called Neural Prediction Model and another called Linear Predictive HMM--are shown to be special cases of the NPHMM proposed here. The experimental result affirms the justification of these proposed models.