A central issue in the analysis of covariance structures is the choice of a suitable model. In this paper two cross-validationCVcriteria are presented for this purpose. For one of these criteria an asymptotically valid approximation is derived. This criterion can be used in conjunction with any correctly specified discrepancy function and is, in comparison with existingCVcriteria, computationally less demanding. The performance of the proposed criterion is evaluated in a Monte Carlo study and compared to the results obtained from various other model-selection criteria, both in small- and large sample situations. An empirical example is given to illustrate its utility in practice. The results demonstrate the effectiveness of the proposedCVcriterion for routinely assessing covariance structural models.