In many cross-cultural research studies, assessment instruments are translated or adapted for use in multiple languages. However, it cannot be assumed that different language versions of an assessment are equivalent across languages. A fundamental issue to be addressed is the comparability or equivalence of the construct measured by each language version of the assessment. This paper presents and critiques several methods for evaluating structural equivalence across different language versions of a test or questionnaire. Applications of these techniques to large-scale, cross-lingual tests are presented and discussed. Simulated data are also used to evaluate the methods. It is concluded that weighted multidimensional scaling and confirmatory factor analysis are effective for helping evaluate construct equivalence across groups. Qualifications for using these procedures to evaluate construct equivalence are provided. (Contains 2 figures, 6 tables, and 42 references.) (Author/SLD)