In this paper we study a model of hypotheses testing consisting of with to simple homogeneous stationary Markov chains ith finite number of states such that having different distributions from four possible transmission probabilities.For solving this problem we apply the method of type and large deviation techniques (LTD). The case of two objects having different distributions from to given probability distribution as examined by Ahlswedeh and Haroutunian.Dans cet article nous ´etudions un mod`ele de tests d’hypoth`eses compos´e de deux chaines de Markov stationnaires homog`enes et simples avec un nombre fini d’´etats ayant diff´erentes distributions parmi quatre probabilit´es de transition possibles. Pour r´esoudre ce probl`eme, nous appliquons la m´ethode des types et des techniques de grandes deviations. Le cas de deux objets ayant diff´erentes distributions issues d’une distribution de probabilit´e donn´ee, a ´et´e examin´e par Ahlswedeh et Haroutunian.Key words: Markov chains; Error probabilities; Different distributions; Transition probabilities; Reliabilities.