This paper considers problems motivated by the dynamic allocation of limited heterogeneous resources in new product development (NPD) projects. The interchangeability of resources and simultaneous resource sharing are defining characteristics of NPD processes. A continuous flow model is introduced that incorporates these features. For problems without activity precedence constraints, a linear program is presented which yields the minimum completion time for all activities. A dynamic, rule-based algorithm is shown to be optimal for two resources processing a multiple-activity arrival stream. For problems with precedence constraints, some special cases are solved, and structural properties of the class of optimal controls for the general problem are discussed.