The agile approach to projects focuses more on close-knit teams than traditional waterfall projects, which means that aspects of group maturity become even more important. This psychological aspect is not much researched in connection to the building of an "agile team." The purpose of this study is to investigate how building agile teams is connected to a group development model taken from social psychology. We conducted ten semi-structured interviews with coaches, Scrum Masters, and managers responsible for the agile process from seven different companies, and collected survey data from 66 group-members from four companies (a total of eight different companies). The survey included an agile measurement tool and the one part of the Group Development Questionnaire. The results show that the practitioners define group developmental aspects as key factors to a successful agile transition. Also, the quantitative measurement of agility was significantly correlated to the group maturity measurement. We conclude that adding these psychological aspects to the description of the "agile team" could increase the understanding of agility and partly help define an "agile team." We propose that future work should develop specific guidelines for how software development teams at different maturity levels might adopt agile principles and practices differently.