This paper concerns the adaptive control problem for a class of discrete-time nonlinear uncertain systems of which the internal uncertainty can be characterized by a finite set of functions. A WLS-like algorithm is used to design the feedback control law, which is tested to be effective and efficient in lots of simulations. It is proved that the closed-loop system is BIBO stable under weak conditions, and two counter-examples are constructed to show that the conditions proposed cannot be removed or weakened in general for this algorithm. (C) 2007 Elsevier Ltd. All rights reserved.