In the years since the printing of my first EQS book in 1994, there has been a steady albeit moderate increase in reported findings from tests for multigroup equiva­ lence. Review of the SEM literature, however, reveals that most tests for invariance have been based on the analysis of covariance structures COVS, as exemplified in chapters 7 and 8. Despite Sorbom’s (1974) introduction of the mean and covari­ ance structures (MACS) strategy in testing for latent mean differences 30 years ago, few studies have been designed to test for latent mean differences across groups based on real (as opposed to simulated) data (see, e.g., Aiken, Stein, & Bentler, 1994; Byrne, 1988b; Cooke et al., 2001; Little, 1997; Marsh & Grayson, 1994; Reise et al., 1993; and Widaman & Reise, 1997). This chapter introduces you to basic concepts associated with the analysis of latent mean structures and walks you through an application that tests for the invariance of latent means across two different cultural groups. Specifically, we test for differences in the latent means of four nonacademic self-concepts (SCs)—Physical SC (Appearance), Physical SC (Ability), Social SC (Peers), and Social SC (Parents)—across Australian and Nigerian adolescents; these constructs comprise the four nonacademic SC compo­ nents of the Self-Description Questionnaire I (SDQ-I; Marsh, 1992). The present application is taken from a study by Byrne and Watkins (2003) but extends this previous work in two ways: (a) analyses are based on MACS rather than only on COVS, and (b) analyses address the issue of missing data with respect to the Nigerian sample (data were complete for the Australian sample).