The dynamic behavior of processing systems exhibits both continuous and significant discrete aspects. Process simulation is therefore a combined discrete/continuous simulation problem. In addition, there is a critical need for a declarative process modeling environment to encompass the entire range of processing system operation, from purely continuous to batch. These issues are addressed by this article.A new formal mathematical description of the combined discrete/continuous simulation problem is introduced to enhance the understanding of the fundamental discrete changes required to model processing systems. The modeling task is decomposed into two distinct activities: modeling fundamental physical behavior, and modeling the external actions imposed on this physical system. Both require significant discrete components. Important contributions include a powerful representation for discontinuities in physical behavior, and the first detailed consideration of how complex sequences of control actions may be modeled in a general manner.