Determination of the proper site for division in Escherichia coli and other bacteria involves a unique spatial oscillatory system in which membrane-associated structures composed of the MinC, MinD and MinE proteins oscillate rapidly between the two cell poles. In vitro evidence indicates that this involves ordered cycles of assembly and disassembly of MinD polymers. We propose a mathematical model to explain this behavior. Unlike previous attempts, the present approach is based on the expected behavior of polymerization-depolymerization systems and incorporates current knowledge of the biochemical properties of MinD and MinE. Simulations based on the model reproduce all of the known topological and temporal characteristics of the in vivo oscillatory system.