This article presents an overview and application of the steps taken in testing for the equivalence of a measuring instrument across one or more groups. Following a basic description of, and rationale underlying these steps, the process is illustrated with data comprising response scores to four nonacademic subscales (Physical SC [Ability], Physical SC [Appearance], Social SC [Peers], and Social SC [Parents]) of the Self Description Questionnaire-I for Australian (N = 497) and Nigerian (N = 439) adolescents. All tests for validity and equivalence are based on the analysis of covariance structures within the framework of CFA models using the EQS 6 program. Prospective impediments to equivalence are suggested and additional caveats proposed in the special case where the groups under study represent different cultures.