The nature of the dynamics of nonverbal interactions is of considerable interest to the study of human communication and future human-computer interaction. Facial expressions constitute an important source of nonverbal social signals. Whereas most studies have focused on the facial expressions of isolated individuals, the aim of this study is to explore the coupling dynamics of facial expressions in social dyadic interactions. Using a special experimental set-up, the frontal facial dynamics of pairs of socially interacting persons were measured and analyzed simultaneously. We introduce the use of convergent cross mapping, a method originating from dynamical systems theory, to assess the causal coupling of the dyadic facial-expression dynamics. The results reveal the presence of bidirectional causal couplings of the facial dynamics. We conclude that convergent cross mapping yields encouraging results in establishing evidence for causal behavioral interactions.