We consider the process algebra BPA* proposed by Bergstra, Bethke, and Ponse, since it nicely defines a class of infinite processes. Investigation of representation of event structures for this class of processes is presented in this article. We extend the algebra BPA* by a parallel composition and modify its sequential operation. For the obtained algebra, named BPA*, we get a correspondence between an algebraic bisimulation defined using the transition systems over BPA*-processes and a behavioural one defined over event structures. This gives us better understanding of the place of event structures among other models of parallelism.