The purposes of this study are to examine the factorial invariance of responses by preadolescent males and females to a multidimensional self-concept instrument, and to demonstrate the use of confirmatory factor analysis (CFA). Sets of responses by 500 males and by 500 females were each randomly divided in half to form four groups (M1, M2, F1, and F2). The factorial invariance of an a priori structure demonstrated the replicability of the structure across the random split halves (M1 and M2, and F1 and F2), and the generality of the structures across opposite-sex comparisons (M1 and F1, and M2 and F2). Additional a posteriori structures that better fit the data were derived on the basis of the initial analyses, but the estimated values of the new parameters were not strictly invariant across either random split halves or opposite-sex comparisons. This suggests that some of the improved fit was illusory and due to capitalizing on chance. However, all opposite-sex comparisons demonstrated the invariance of factor loadings and factor correlations for a priori and a posteriori structures. A three-page list of bibliographical references and the tabulated data follow the report. (Author/JAZ)