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The problem of finding an optimal dynamic assignment of a modular program for a two-processor system is analyzed. Stone's formulation of the static assignment problem is extended to include the cost of dynamically reassigning a module from one processor to the other and the cost of module residence without execution. By relocating modules during the course of program execution, changes in the locality of the program can be taken into account. It is shown that network flow algorithms may be used to find a dynamic assignment that minimizes the sum of module execution costs, module residence costs, intermodule communication costs, and module reassignment costs. Techniques for reducing the size of the problem are described for the case where the costs of residence are negligible.