Holding an intention often interferes with other ongoing activities, indicating that resource-demanding processes are involved in maintaining the intention and noticing the appropriate event to fulfill it. Little is known, however, about the nature of the processes underlying this task interference effect. The goal of the present research was to decompose the processes contributing to the task interference effect by applying the diffusion model (Ratcliff, Psychological Review 85:59-108, 1978) to an event-based prospective memory task. In the first experiment, we validated the interpretation of the response criterion parameter (a) of the diffusion model as reflecting strategies to cope with the anticipated demands of a prospective memory task in the context of the ongoing task. The second experiment served to investigate which underlying processes contribute to the task interference often found with prospective memory tasks. Diffusion model analyses revealed that the task interference effect was due to (1) less efficient processing in the more demanding than in the less demanding prospective memory task and (2) a more conservative response criterion. We suggest that the anticipated demands and the additional processing demands of the prospective memory task jointly contribute to the task interference effect.