Discrete-time sliding mode control is considered. The case of known parameters is first analyzed, leading to a new definition of the so-called ’equivalent control’ as the piecewise-constant control that reduces to zero, in finite time, the distance of the system state from the sliding manifold. In the presence of bounded parametric uncertainties, an adaptive control scheme that guarantees the asymptotic satisfaction of the same control objective is presented. The main feature of this approach is the reduction of the order of the relevant error equation, and the possibility of dealing with the nonmatched uncertainties introduced by the sampling process.