A collection of basic ideas is presented, which have been involved by various workers over the past four years to provide a suitable framework for the design and analysis of multiprocessing systems. The notions of process and state vector are discussed, and that the nature of basic operations on processes is considered. Some of the connections between processes and protection are analyzed. A very general approach to priority-oriented scheduling is described, and its relationship to conventional interrupt systems is explained. Some aspects of time-oriented scheduling are considered. The implementation of the scheduling mechanism is analyzed in detail and the feasibility of embodying it in hardware established. Finally several methods for interlocking execution of independent processes are presented and compared.