The present study investigates the sensitivity of distinct brain regions to the syntactic processing of running speech. Experimental conditions varied the grammaticality of sentence types (correct vs. incorrect). Moreover, two different groups of subjects listened to the same sentence material, but followed two different task instructions. All participants were asked to listen to the auditory stimuli and to perform in a grammaticality judgment-task, whereas only half of the subjects were instructed to additionally repair incorrect sentences covertly. Significantly increased brain responses occurred in several left temporal areas as a function of sentences’ grammaticality, particularly, in the ‘pure’ judgment-group. Spatial extent as well as the strength of focal brain activation changed as a function of grammaticality and task demand. A generally enhanced pattern of local blood supply to the right peri-sylvian cortex could be observed when individuals additionally realized the repair-task. In particular, the right inferior frontal gyrus (pars opercularis and pars triangularis) and the right temporal transverse gyrus (Heschl's gyrus) were more strongly affected by the repair-task demand. In contrast, an anterior portion of the superior temporal gyrus (planum polare) displayed increased activation bilaterally. Although left hemisphere activation varied clearly as a function of a sentence's grammaticality, the present findings demonstrate an involvement of the right peri-sylvian cortex, in particular, when task demands explicitly require an on-line repair. The results as a whole suggest a reconsideration of the notion that auditory language comprehension is restricted to the left hemisphere. The underlying mechanisms and the respective roles of both the left and the right hemisphere during speech processing are discussed.