The use of formative and shared or co-assessment has been shown to improve the motivation, involvement and learning of university students. The aim of this study is to analyse the effect that implementing these processes has on university students' perception of their acquisition of transversal competences. The participants in the study were 1021 students from five Spanish universities taking degree courses in primary education or physical education and sport science. They all experienced formative and shared or co-assessment throughout a complete academic year of their courses. For the data collection, a Self-Perception Scale of Transversal Competences was created, which had adequate values of reliability and validity. Using a transversal design (inter-subjects), inferential statistical analysis was undertaken of the differences in means between the perception of a range of transversal competences before and after the course. The results show significant perceived improvements at the end of the course for most of the competences analysed, which indicates, among other thing, the value and importance of this type of assessment for the educational process.