The ventral premotor cortex (PMv) and the primary motor cortex (MI) of monkeys participate in various sensorimotor integrations, such as the transformation of coordinates from visual to motor space, because the areas contain movement-related neuronal activity reflecting either visual or motor space. In addition to relationship to visual and motor space, laterality of the activity could indicate stages in the visuomotor transformation. Thus, we examined laterality and relationship to visual and motor space of movement-related neuronal activity in the PMv and MI of monkeys performing a fast-reaching task with the left or right arm, toward targets with visual and motor coordinates that had been dissociated by shift prisms. We determined laterality of each activity quantitatively, and classified it into four types: activity that consistently depended on target locations in either head-centered visual coordinates (V-type) or motor coordinates (M-type), and those that had either differential or non-differential activity for both coordinates (B- and N-types). A majority of M-type neurons in the areas had preferences for reaching movements with the arm contralateral to the hemisphere where neuronal activity was recorded. In contrast, most of the V-type neurons were recorded in the PMv, and exhibited less laterality than the M-type. The B- and N-types were recorded in the PMv and MI, and exhibited intermediate properties between the V- and M-types when laterality and correlations to visual and motor space of them were jointly examined. These results suggest that the cortical motor areas contribute to the transformation of coordinates to generate final motor commands.