The notion of confluence is studied on the context of bigraphs. Confluence will be important in modelling real-world systems, both natural (as in biology) and artificial (as in pervasive computing). The paper uses bigraphs in which names have multiple locality; this enables a formulation of the lambda calculus with explicit substitutions. The paper reports work in progress, seeking conditions on a bigraphical reactive system that are sufficient to ensure confluence; the conditions must deal with the way that bigraphical redexes can be intricately intertwined. The conditions should also be satisfied by the lambda calculus. After discussion of these issues, two conjectures are put forward.