Since the pioneer work of K. J. Aström and B. Wittenmark on self-tuning regulators [Automatica 9, 185-199 (1973; Zbl 0249.93049)] there have been published a lot of works on stochastic adaptive tracking, in particular the problem of identifying unknown parameters and simultaneously tracking a reference signal has been completely solved for linear models. For nonlinear models several methods have been proposed, but theoretical results for them are not always proven. The present paper focuses its attention on NARX models on \(\mathbb{R}^d\) of the form \(X_{n+1}= f(X_n)+ U_n+ \xi_{n+1}\), \(n\geq 1\), where the state \(X_n\) is observed, the driving function \(f\) is unknown, \(\xi_n\) is an unobservable white noise, and the control \(U_n\) is chosen in order to track a given deterministic reference trajectory. The authors estimate \(f\) by introducing a kernel method-based recursive estimator [W. Härdle, “Applied nonparametric regression” (1990; Zbl 0714.62030); L. Devroye and L. Györfi, “Nonparametric density estimation” (1985; Zbl 0546.62015)]. They study two adaptive control laws built from this nonparametric estimator and derived from the self-tuning control. The first one can be used for open-loop systems and requires an additional exciting noise. The second one needs some a priori information on \(f\) but allows to control open-loop unstable systems. The authors prove the almost sure convergence of the nonparametric estimator of \(f\) over dilating sets and prove that both adaptive control laws are asymptotically optimal in quadratic mean. Finally, they give a strongly consistent estimator of the covariance matrix of \(\xi_n\).