A direct adaptive control is presented in this paper for the control of a class of discrete-time nonlinear systems which include many useful models well known in the literature. The asymptotic stability and global convergence of the algorithm proposed in this paper have been established under mild regularity assumptions. A concept of the so-called stronger left coprime is first introduced in this paper. It is shown that the concept plays a crucial role in the problems of stabilizing a system and realizing the adaptive control algorithm.