Asymptotically universally efficient estimators of the parameters in the general linear hypothesis are proposed. These estimators are based on ranks of residuals (or their absolute values); they are analogous to the linearized rank estimators proposed by Kraft and van Eeden in the sense that they are obtained by replacing, in these estimators, the function generating the scores by certain estimators of this function. Finally, it is shown that estimators of the score function, satisfying the conditions used, exist.