Task-dependent exogenous cuing effects on reaction time in detection and discrimination tasks have been ascribed to delayed withdrawal of attention in discrimination tasks. Alternatively, these differences may be due to cue-induced response inhibition in detection tasks. Unimodal and crossmodal versions of the Posner paradigm were examined with short cue-target intervals. Targets above or below fixation required either detection or discrimination responses. Cuing effects were determined for the target-elicited P1 component and for the lateralized readiness potential (LRP). Task-dependent cuing effects on reaction time were found in the unimodal but not in the crossmodal version, but not for the P1 component. The LRP data indicated that inhibition of return in the unimodal detection task had a premotoric locus. These findings suggest that inhibition in the unimodal detection task resulted from speeded motor inhibition triggered by the visual cue.