A number of estimators of parameters in nonlinear models have been proposed in the econometric literature. Various specialized methods have been developed to demonstrate the consistency of the suggested estimators. The first part of this paper presents a general scheme of the consistency proof. This method can be used to prove consistency of the large class of estimators of parameters in nonlinear regression models and nonlinear simultaneous equation models. The second part of this paper utilizes this general method to demonstrate the consistency of maximum likelihood estimators of nonlinear regression models with autocorrelated errors.