A class of decompositions is derived for the variance-covariance matrix @W of a generalized error components model, introduced in [18 and 19]. The spectral decomposition of @W is a member of this class. For estimation purposes certain other members of the class are preferred, especially those that allow for simplifying transformations of the model not depending on unknown parameters. The transformations suggest simple and asymptotically efficient estimators of both the parameters in @W and the parameters in the systematic part of the model.