A fundamental problem that must be addressed by connectionism is that of creating and representing dynamic structures (Feldman 1982; von der Malsburg 1985). In the context of reasoning with systematic and abstract knowledge, this problem takes the form of the variable binding problem. We describe a biologically plausible solution to this problem and outline how a knowledge representation and reasoning system can use this solution to perform a class of predictive inferences with extreme efficiency. The proposed system solves the variable binding problem by propagating rhythmic patterns of activity wherein dynamic bindings are represented as the synchronous firing of appropriate nodes.