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In this paper, we design a discrete-time sliding mode (DSM) nonlinear observer for a class of nonlinear uncertain systems. Taylor series expansion together with a nonlinear state transformation is used to discretize the system. A strategy to avoid switching across the sliding manifold is employed, and the sliding trajectory is confined to a boundary layer once it converges to the sliding manifold. We call this phenomenon DSM. The conditions for existence of DSM are derived. The condition for the asymptotical stability of the estimation error is analyzed.