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In linear filtering, the set-membership normalized least mean squares (SM-NLMS) algorithm has been shown to exhibit desirable features of selective update and optimized variable step size. In this paper, a kernel approach to the SM-NLMS algorithm is presented that makes it feasible to address nonlinear problems. An online greedy approximation technique to achieve sparsity is discussed. Simulation results are presented for two practical problems: equalization of nonlinear inter-symbol interference (ISI) channels and predistortion of nonlinear high power amplifiers (HPA).