Previous studies have shown that asymmetries in upper limb sensorimotor function are dependent on the source of sensory and motor information, hand preference and differences in hand strength. Further, the utilization of sensory and motor information and the mode of control of force may differ between the right hand/ left hemisphere and left hand/ right hemisphere systems. To more clearly understand the unique contribution of hand strength and intrinsic differences to the control of grasp force, we investigated hand/ hemisphere differences when the source of force information was encoded at two different force levels corresponding to a 20 and 70% maximum voluntary contraction or the right and left hand of each participant. Eleven, adult males who demonstrated a stronger right than left maximum grasp force were requested to match a right or left hand 20 or 70% maximal voluntary contraction reference force with the opposite hand. During the matching task, visual feedback corresponding to the production of the reference force was available and then removed when the contralateral hand performed the match. The matching relative force error was significantly different between hands for the 70% MVC reference force but not for the 20% MVC reference force. Directional asymmetries, quantified as the matching force constant error, showed right hand overshoots and left undershoots were force dependent and primarily due to greater undershoots when matching with the left hand the right hand reference force. Findings further suggest that the interaction between internal sources of information, such as efferent copy and proprioception, as well as hand strength differences appear to be hand/ hemisphere system dependent. Investigations of force matching tasks under conditions whereby force level is varied and visual feedback of the reference force is available provides critical baseline information for building effective interventions for asymmetric (stroke-related, Parkinson's Disease) and symmetric (Amyotrophic Lateral Sclerosis) upper limb recovery of neurological conditions where the various sources of sensory -motor information have been significantly altered by the disease process.