HYPE is a process algebra for hybrid systems. It models the flows that affect the continuous aspects of the system and allows for discrete events to occur which may change the flows. The operational semantics define a transition system labelled with events, and the states of this transition system can be used to obtain the ordinary differential equations (ODEs) which describe the continuous change of the hybrid system. For well-defined HYPE models, system-bisimilar models have the same ODEs. Semantic equivalences such as bisimulation have also been defined for other process algebras for hybrid systems and these are considered in the context of HYPE together with new equivalences for HYPE.