The Sequential Probaility Ratio Test is applied to test two simple hypotheses about the transition probability matrix of an irreducible homogeneous MARKOV chain with finite state space. An analogue (14) of Wald's Fundamental Identity, the Operating Characteristic Function (20-21) and the Average Sample Number (22-23) are given. These statements are generalizations of the MARKOV chain as well as some more conditions about the eigenvalues of the transition probability matrix.