The paper first identifies the concurrency requirements for a high-level concurrent programming language, and then discusses how the concurrency primitives proposed for the programming language Ada meet these requirements. This is followed by a description of an actual implementation of the Ada tasking constructs on a distributed multiprocessor computer system comprising a number of multiprocessor-shared memory stations linked by a serial communications network. A brief description of the system and the overheads involved when implementing the rendezvous mechanism on this architecture is presented, and also the implications of processing interrupts by mapping them into external entry calls to high-level service tasks are discussed