A classical theorem states that the set of languages given by a pushdown automaton coincides with the set of languages given by a context-free grammar. In a recent article, Bas Luttik and I proved the pendant of this theorem in a setting with interaction: the set of processes given by a pushdown automaton coincides with the set of processes given by a finite guarded recursive specification over a process algebra with actions, choice, and sequencing with sequential value passing. In a current paper, we look what happens if we consider parallel pushdown automata instead of pushdown automata, and a process algebra with parallelism instead of sequencing.