In this paper the discrete-time analog of the input-to-state stability condition introduced by Sontag for the continuous-time case is presented together with two theorems dealing with global stabilization of discrete-time systems. The corresponding proofs are discrete analogs of those presented for the continuous-time case in [5], [8], [9]. It is shown that the assumptions of the main results for the discrete-time case are weaker than those imposed in the continuous-time case.