Exchanges are controlled by processors which comprise logical switching and memory apparatus. The total processing is divided, for economy, between groups of processors, each associated with a transmission circuit or trunk in the exchange. The processors necessary for the control of a connection thus become associated as the connection is built up. Further economy results from the time sharing of a smaller number of processors among the circuit processors of a group by parallel connection, when required, through an interface switch. Electronic devices add time-division time sharing to space-division time sharing and stored-program logic to wired-logic techniques that are already well established in telephone-exchange control systems. Processors and processing in general, and the principles of division for series operation and for time-shared parallel operation, with special reference to the new conditions created by electronic devices, are analysed and defined. Wired and stored-program logic processors are compared, with the conclusion that wired logic should continue as the basis for exchange control systems, but with a backing of stored-program processors for operations that do not greatly affect the economics of exchanges, and for which the flexibility of stored-program logic is an advantage. The conclusions are the basis for exchange systems described in other papers.