The problem of estimation of the function \(F(\theta_0'x +m_0(z))\) is solved, where \(F:R\to R\) is a given function, \(\Theta_0\in R^{d_1}\) an unknown parameter, and \(M_0 (z)\) an unknown function in a given class of functions. The authors propose quasi-likelihood estimators as estimators of the unknown characteristics basing on a sample from the random vector \((Y,T)\), where \(T= (X,Z)\), \(X\in R^{d_1}\) and \(Z\in R^{d_2}\). The statistical properties of the proposed estimators are studied. In particular, asymptotic normality and consistency are proved.