Hidden Markov model is a statistical model which has been applied successfully to speech recognition and natural language processing. However, it is based on three assumptions: (1) limited horizon, (2) time invariant (stationary), (3)the independence assumption of observations within a state. These assumptions are too strong from the view of the statistics and are also unreaistic. In order to overcome the defects of the classical HMM, Markov Family model, a new statistical models is proposed in this paper. The speaker independent continuous speech recognition experiments and the Part-of-Speech tagging experiments show that Markov Family models (MFMs) have higher performance than Hidden Markov models (HMMs).