This paper extends the power hierarchy of dependability models developed by Malhotra and Trivedi (1994) and Muppala et al. (2000) to include Piecewise Deterministic Markov Processes (PDP) and PDP-related Petri Nets. PDPs are known as the largest class of continuous-time hybrid state Markov processes not involving diusions. Since Petri Nets have proven to be extremely useful in developing Markov process models of complex practical processes, there is a clear need for a type of Petri Net that can play such role for developing PDP models. This paper defines such Petri Nets and shows their relation to PDPs and other Petri Nets.