Summary: The focus of this paper is the nonparametric estimation of an instrumental regression function \(\varphi\) defined by conditional moment restrictions that stem from a structural econometric model \(E[Y - \varphi (Z)|W]=0\), and involve endogenous variables \(Y\) and \(Z\) and instruments \(W\). The function \(\varphi\) is the solution of an ill-posed inverse problem and we propose an estimation procedure based on Tikhonov regularization. The paper analyzes identification and overidentification of this model, and presents asymptotic properties of the estimated nonparametric instrumental regression function.