In this paper, we first study the strong law of large
numbers for the frequencies of occurrence of random ordered couples of states
for nonhomogeneous bifurcating Markov chains indexed by a binary tree. Then
the strong law of large numbers are studied for functions of the nonhomogeneous
bifurcating Markov chains indexed by a binary tree. As a corollary, we obtain
the shannon-McMillan theorem for these Markov chains with finite state space.