This study has three main objectives. The first is to know to which degree engagement, as a person variable, and each of its modalities--agency, behavior, cognition, and emotion--are affected by the interaction with several learning situations, listening to a lecture, carrying out practical tasks alone, reading a text while studying, working in groups, or participating in practical classes. The second is to test its relationships with potential moderator variables--motivation, self-efficacy, emotion self-regulation, and stress--and its potential effects on performance and satisfaction. Participants were 531 university students. They filled in a questionnaire that allowed testing alternative theoretical models on the person-situation hypothesis using confirmatory factor analyses. Results showed that if items refer both to engagement modalities and learning situations, the traditional hierarchical model that considers that engagement depends on a personal disposition with four components does not fit well. Instead, the multitrait model does. It shows that engagement, as a general disposition, is activated by the set of situations and that each of its components only plays a role in some of them. The hypotheses on the relationship between engagement and the rest of the variables received positive support. These results open new perspectives for studying and improving engagement.