The student engagement framework, originally developed for the US educational system, has become increasingly recognised internationally as a means of fostering learning gains in higher education. Despite its recognition, some researchers raise a question about the applicability of this framework in other cultural contexts. Our research extends the existing literature on student engagement by filling the gap of knowledge about the cross-cultural applicability of the student engagement framework. Utilising multi-group structural equation modelling, this paper answers the question about the national differences in associations between student engagement dimensions and the development of generic skills. Data collected from 21 universities across the U.S.A., China, Japan, and Russia, were used. Relying on student engagement literature, four student engagement dimensions were constructed: (1) class engagement, (2) extra effort to meet course objectives or own learning tasks, (3) disengagement, and (4) collaborative learning. The findings support multi-group invariance of the associations between student engagement dimensions and the perceived gains in generic skills across all participating countries. Regardless of country specifics, the extra effort and collaborative learning significantly contribute to the development of generic skills while disengagement has a negative effect.