Abstract. Parallel systems which include priority can experience conflicts when two concurrent processes assign different priorities to the same actions. There are at least two ways to resolve the difficulty: one is to halt; the other is to declare a draw and allocate all the offending actions the same priority. In CSPP these are called respectively hard and soft priority.

Originally CSPP included only hard priority. Here we extend the language to include soft priority as well. The Acceptances semantics which is used to define CSPP does not require modification: it captures both soft and hard behaviours.