The main objective of this paper is to put forward a software process model for high-performance systems (HPS), and to present a formal framework to describe software design methodologies (SDMs) for those systems. The framework consists of two main parts: the software process activities which characterise the development of HPS, and the components of the SDM (concepts, artifacts, representation and actions) which are essential for any methodology. The framework relates these two parts by identifying generic components of each activity in the software process that can be used to classify and evaluate SDMs for HPS. The framework has been formally specified using the language Z and used to derive formal specifications of SDMs. This is illustrated in the paper by presenting part of the specification of oDM (an occam design method).