Add to ORKGAbstract. CPDPs (Communicating Piecewise Deterministic Markov Processes) can be used for compositional specification of systems from the class of stochastic hybrid processes formed by PDPs (Piecewise De-terministic Markov Processes). We define CPDPs and the composition of CPDPs, and prove that the class of CPDPs is closed under composition. Then we introduce a notion of bisimulation for PDPs and CPDPs and we prove that bisimilar PDPs as well as bisimilar CPDPs have equal stochas-tic behavior. Finally, as main result, we prove the congruence property that, for a composite CPDP, substituting components by different but bisimilar components results in a CPDP that is bisimilar to the original composite CPDP (and therefore has equal stochastic b...