The paper addresses the automatic recognition of social and task-oriented functional roles in small-group meetings, focusing on several properties: a) the importance of non-linguistic behaviors, b) the relative time-consistency of the social roles played by a given person during the course of a meeting, and c) the interplays and mutual constraints among the roles enacted by the different participants in a social encounter. In particular, this paper proposes that the Influence Model framework can address these properties of functional roles, and compares the performance obtained by this framework to the performances of models that consider only property (a) (SVM), and to those that address both (a) and (b) (HMM). The results obtained confirm our expectations: the classification of social functional roles improves if models account for temporal dependencies among the roles played by the same subject, for the time properties of the roles played by each individual, and for the mutual constraints among the roles of different group members. The two versions of the Influence Model (IM and newIM), which encode all three properties together, outperform both the SVM and the HMM on most of the figures of merit used. Of particular interest is the capability of the Influence Model to obtain good or very good results on the less-populated classes-Orienteer and Seeker for the task area, and Attacker and Supporter for the socio-emotional area.