Recent work by van Glabbeek and coauthors suggests that the liveness property for Peterson’s mutual exclusion algorithm, which states that any process wanting to enter the critical section will eventually enter it, cannot be analysed in CCS and related formalisms. In our article, we explore the formal underpinning of this suggestion and its ramifications. In particular, we show that the liveness property for Peterson’s algorithm can be established convincingly with the mCRL2 toolset, which has a conventional ACP-style process-algebra based specification formalism.