A notion of bigraph is introduced as a model of mobile interaction. A bigraph consists of two independent structures: a topograph representing locality and an edge net representing connectivity. Bigraphs arc equipped with reaction rules to form bigraphical reactive systems (BRSs), which include versions of the π-calculus and the ambient calculus. A behavioural theory is established, using the categorical notion of relative pushout; it allows labelled transition systems to be derived uniformly for a wide variety of BRSs, in such a way that familiar behavioural prcordcrs and equivalences, in particular bisimilarity, are congruential. An example of the derivation is discussed.