We asked which brain areas are engaged in the coordination of our hands in dexterous object manipulations where they cooperate for achieving a common goal. Well-trained right-handers steered a cursor on a screen to hit successively displayed targets by applying isometric forces and torques to a rigid tool. In two bimanual conditions, the object was held freely in the air and the hands thus generated coupled opposing forces. Yet, depending on the mapping rule linking hand forces and cursor movements, all subjects selected either the left or the right hand as prime actor. In two unimanual conditions, the subjects performed the same task with either the left or the right hand operating on a fixed tool. Functional magnetic resonance imaging revealed common activation across all four conditions in a dorsal fronto-parietal network biased to the left hemisphere and in bilateral occipitotemporal cortex. Contrary to the notion that medial wall premotor areas are especially active in complex bimanual actions, their activation depended on acting hand (left, right) rather than on grip type (bimanual, unimanual). We observed effects of grip type only in the primary sensorimotor cortex (SMC). In particular, with either hand as prime actor, bimanual actions preferentially activated subregions of the SMC contralateral to the acting hand. A sizeable subregion with preference for unimanual activity was found only in the left SMC in our right-handed subjects. Collectively, these results indicate a hemispheric asymmetry for the SMC and that partially different neural populations support the control of bimanual versus unimanual object manipulations.