This paper presents a class of robust estimators for linear and non-linear simultaneous equations models, which are a direct generalization of the maximum likelihood estimator. The new estimators are obtained as solutions of a generalized likelihood equation. They are resistant to deviations from the model distribution, to outlying observations, and to some model misspecifications. An optimality principle leads to the construction of an optimal robust estimator which is the best trade-off between efficiency at the model and robustness.