One of the most important tasks in the analysis of a non-linear system is lo determine its global behaviour and, in particular, to delineate the domains of attraction for asymptotically stable solutions. Stable manifolds often act as boundary surfaces between such domains in the state space.In this paper the morphology of boundary surfaces is studied in a single member of Chua's circuit family, although the techniques used apply equally well to many other non-linear circuits. On the way, an answer is given to a former question of Matsumoto et a / . concerning boundary surfaces in a chaotic circuit.Dynamical properties of a sequential circuit can be investigated by means of switching between the system's attractors, and boundary surfaces play a crucial role in the process of switching. As an application of the boundary surface techniques, dynamical properties of two models for ternary logic are presented and analysed.