Understanding speech from different speakers is a sophisticated process, particularly because the same acoustic parameters convey important information about both the speech message and the person speaking. How the human brain accomplishes speech recognition under such conditions is unknown. One view is that speaker information is discarded at early processing stages and not used for understanding the speech message. An alternative view is that speaker information is exploited to improve speech recognition. Consistent with the latter view, previous research identified functional interactions between the left- and the right-hemispheric superior temporal sulcus/gyrus, which process speech- and speaker-specific vocal tract parameters, respectively. Vocal tract parameters are one of the two major acoustic features that determine both speaker identity and speech message (phonemes). Here, using functional magnetic resonance imaging (fMRI), we show that a similar interaction exists for glottal fold parameters between the left and right Heschl's gyri. Glottal fold parameters are the other main acoustic feature that determines speaker identity and speech message (linguistic prosody). The findings suggest that interactions between left- and right-hemispheric areas are specific to the processing of different acoustic features of speech and speaker, and that they represent a general neural mechanism when understanding speech from different speakers.