In this paper THEIL'S mixed estimator (THEIL 1963) is generalized so that all the full rank assumptions of the original definition are removed. Necessary and sufficient conditions are proved for superiority of a generalized mixed estimator over another generalized mixed estimator with respect to covariance matrix for all estimable parametric functions K?. Corresponding generalized results for several important subclasses of mixed estimators, as for restricted least squares estimators, are obtained. It is alos pointed out, that similar kindsl of weaker superiority statements can be proved for a fixed parametrie function K?