In task switching, the n-2 repetition cost (informally, the elevation in RT associated with performing a recently abandoned task) is an indicator of residual task-set inhibition. One suggestion is that such inhibition is triggered by conflict between task-set elements. We present a novel computational model instantiating this proposal, by adding task-conflict monitoring units to an existing, interactive activation model of task switching. The model produces the empirical pattern, n-1 switch costs and n-2 repetition costs, as an intrinsic property of its architecture, but dependent on the inhibition of task demand units by the conflict detection mechanism. In a further simulation, we make predictions about n-2 repetition costs for asymmetric tasks, and show that one functional benefit of such a conflict-based, task inhibition mechanism is to facilitate topdown control of tasks by automatically reducing cross-task interference