Considering a dyad as a dynamic system whose current state depends on its past state has allowed researchers to investigate whether and how partners influence each other. Some researchers have also focused on how differences between dyads in their interaction patterns are related to other differences between them. A promising approach in this area is the model that was proposed by Gottman and Murray, which is based on nonlinear coupled difference equations. In this paper, it is shown that their model is a special case of the threshold autoregressive (TAR) model. As a consequence, we can make use of existing knowledge about TAR models with respect to parameter estimation, model alternatives and model selection. We propose a new estimation procedure and perform a simulation study to compare it to the estimation procedure developed by Gottman and Murray. In addition, we include an empirical example based on interaction data of three dyads.Key words: dynamic system, TAR model, autoregressive, dyadic interaction.The notion of a dynamic system has become increasingly popular in psychology, both as a metaphor and as a quantitative approach. Recently, there has been a burst of applications, for instance in the study of development (Thelen & Smith, 1994;Van der Maas & Molenaar, 1992;Van Geert & Van Dijk, 2002), self-regulation of behavior (Carver & Scheier, 1998), personality (Shoda, Tiernan, & Mischel, 2002), addiction (Warren, Hawkins, & Sprott, 2003;Witkiewitz, Van der Maas, Hufford, & Marlatt, 2007), grief (Bisconti, Bergeman, & Boker, 2004), psychopathology (Granic & Hollenstein, 2003), and psychotherapy (Schiepek, 2003). In addition, several leading journals have devoted special issues to the topic (Vallacher & Nowak, 1997;Vallacher, Read, & Nowak, 2002), and in 1997 a new journal called Nonlinear Dynamics, Psychology, and Life Sciences was started (Guastello, 1997).Mathematically, a dynamic (or dynamical) system is a set of equations that expresses how the state of a system (represented by one or more variables) changes as a function of its previous state. These equations may be deterministic or stochastic (Clayton, 1997), and they can be defined in continuous time as differential equations, or in discrete time as difference equations. A particularly useful application of dynamic system theory in psychological research concerns the study of dyadic interactions: Representing each partner by one or more variables and measuring them repeatedly over time allows the researcher to determine whether and how the partners influence each other.