Consistent estimators for linear and nonlinear regression models with measurement errors in variables in the presence of validation data are proposed. The estimation procedures are based on least squares methods with regression functions replaced by wide-sense conditional expectation functions. The methods do not depend on distributional assumptions and are robust against the misspecification of a measurement error model. They are computationally and analytically simpler than semiparametric methods based on nonparametric regression or density functions.