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In this paper, we formulate mathematical model to describe the interaction of two strains of HIV virus and the target cells within a host. Model is in the form of a delay differential equations with a two discrete delays to account for the average time for replication for the two strains. The model dynamical turns to be generically determined by two composite parameters R1 and R2, the basic reproduction numbers for strain 1 and strain 2 in the absence of the other strain, in the sense that except for the critical case R1 = R2 > 1, the solutions are proved to converge to the corresponding equilibrium globally. The method used is Lyapunov functionals.