Causal consistent reversibility blends causality and reversibility. For a concurrent system, it says that an action can be undone provided this has no consequences, thereby making it possible to bring the system back to a past consistent state. Time reversibility is considered instead in the performance evaluation field. A continuous-time Markov chain is time reversible if its behavior remains the same when the direction of time is reversed. We try to bridge these two theories by showing the conditions under which both causal consistent reversibility and time reversibility can be achieved in the setting of a stochastic process algebra.