This study investigates the phases of development of synchronous and asynchronous virtual communication produced in a community of inquiry (CoI) by analyzing the internal structure of each intervention in the forum and each chat session to determine the evolution of their social, cognitive and teaching character. It also analyzes the participating higher education students' satisfaction with the activities, with the professors' actions, and with themselves. We use a mixed methodology that includes content analysis of the virtual communications by crossing two categorization systems: (1) type of communication according to the model adopted from Garrison, Anderson and Archer (social, cognitive and teaching presence) and (2) phases in the evolution of the communication (initiation, proposal, development, opinion/closing and good-byes). The data are relevant to the students' satisfaction and grades earned. The results suggest differences in the quantity and content of the communication in each phase and an evolution from social to cognitive elements, ending with social contributions. The students are satisfied with the virtual communications related to both the activities and the professors and evaluate themselves positively.