This paper outlines how Rasch modelling can be used for testing assumption about measurement equivalence in international studies. Based on the Rasch model (Rasch, 1960) for dichotomous items and the Partial Credit model for polytomous items (Masters & Wright, 1982), so-called item-by-country interactions can be estimated that provide useful information about the level of measurement invariance in parameter estimates. It should be noted that item-by-country interactions are one form of differential item functioning (DIF) where groups vary in their probability of answering questions even after controlling for their levels of ability (see Hambleton, Swaminathan and Rogers, 1991). Item-by-country interactions can be obtained from comparing separate calibrations for national sub-samples or estimated directly through the inclusion of additional model parameters (see examples in Walker, 2007 and Schulz, 2009). Using field trial data from the IEA International Civic and Citizenship Education Study (ICCS) this paper outlines ways of obtaining estimates of measurement invariance and discusses their interpretations as well as limitations of these analyses. In particular, the paper illustrates the analysis of item-by-country interactions for test items and the estimation of country effects when scaling questionnaire (Likert-type) items.