Patients with focal lesions in the left (n = 7) and right (n = 4) prefrontal cortex were compared with controls (n = 16) in a task-switching experiment using four different, simple spatial tasks. Each of these tasks involved a left-right decision, either regarding an arrow, the word “left” or “right”, a circle position, or the direction of a moving line. We compared performance on trials that required rule switches versus rule repetitions (local switch costs) and we compared performance between blocks with bivalent stimuli (two dimensions present) and blocks with univalent stimuli (only one dimension present) to assess global switch costs. Patients with left prefrontal lesions, but not patients with right prefrontal lesions, exhibited increased costs on trials in which the relevant dimension switched (local switch costs), but also on no-switch trials with bivalent stimuli (global costs). We also assessed task-set inhibition in the form of the backward-inhibition effect [increased response times to recently abandoned tasks; Mayr, U., & Keele, S. Changing internal constraints on action: The role of backward inhibition. Journal of Experimental Psychology: General, 129, 4-26, 2000]. Although left frontal patients showed normal inhibition, right frontal patients showed no evidence for inhibition. These results suggest a neurocognitive dissociation between task-set selection and inhibition.