We present some statistical results on nonlinear adaptive control using kernel estimators. We are concerned with a nonlinear autoregressive model of the form Xn+1 = f(X-n) + U-n + xi (n+1), n is an element of N, controlled using a nonparametric estimator of the unknown function f and derived from a tracking control policy. We prove an almost sure convergence result for the noise density estimator, a pointwise central limit theorem for f, and a test for linearity of the driving function f.