Abstract: In this paper we study the asymptotic equipartition property （AEP） for nonhomogeneous Markov information sources. We first give a limit theorem for the averages of the funcitions of two variables of the information sources by using the convergence theorem for martingale difference sequences. As corollaries of the main result, we get several limit theorems and a limit theorem of the relative entropy densities which hold for any nonhomogeneous Markov information source,Finally, we prove the AEP for a class or nonhimogeneous Markov information sources