Dialogue has been formalized with P systems in [4] as a sequential event, as it is usually considered and tackled. In this paper, we remark that conversation can be somehow understood as a parallel interaction between agents. P systems, which are by definition parallel devices, provide a suitable framework to model such non-standard conversational phenomena. Two parallel events in dialogue: immediate reply and overlapping are explained from a realistic pragmatic perspective, and formal descriptions for them are introduced.