Abstract: Some basic concepts on the states, such as strongly recurrent state, weakly recurrent state, and strongly transient state, were proposed, and the corresponding Character number L(x,0;F) and G(x,0;F) were studied. On the base of this, Criteria for the states to be accesible and uniformly accesible were given. The results generalized the corresponding results in classical Markov chains.

Key words: strongly recurrent state, strongly transient state, weakly recurrent state, skew product Markov chains, strongly recurrent state, strongly transient state, weakly recurrent state