Parallel high-performance computing is gaining momentum as a computing platform for many applications. In recent years, the research in software support for parallel computers has mainly addressed scientific and information processing applications. Very little attention has been paid to real-time embedded system requirements on parallel machines. This research investigates some important issues related to designing real-time system software for parallel computers. In this paper, we discuss a formal specification language for real-time systems on parallel architectures. Towards this end we propose the Parallel REal Time SpEcification Language (PRETSEL). We discuss the computation model on which PRETSEL is based, its syntax, its semantics, and its applicability. PRETSEL extends existing algebraic models by providing structured timing constructs, communication primatives and explicit parallelism constructs.