Hand skill was analyzed using a computerized peg moving task. The durations of single hand movements (PMTs) were accurately measured in right-hand (RH) and left-hand (LH) writers. One trial consisted of 10 movements of the right hand and 10 movements of the left hand. Each participant performed five trials. Women showed significantly higher percentage than men in right-handedness; men showed higher percentage than women in left-handedness. This sex difference completely disappeared after taking the same height range in participants. The mean RH- and LH-PMTs decreased in 5 successive trials, even within a single trial during 10 successive hand movements, indicating a learning effect of repeated hand movements. The LH- minus RH-PMTs exhibited fluctuations within a single trial between positive (faster right hand) and negative (faster left hand) values. LH-RH PMTs were significantly greater than zero, in favor of right hand, in RH-writers, but not significantly different from zero in LH-writers, exhibiting a true fluctuating asymmetry. Participants with no familial sinistrality (FS-) were preponderantly fight-handed (ca. 90%), those with left-handed mother and right-handed father (FS+1) showed stochastic distribution of hand preference (50:50). Participants with right-handed mother and left-hander father (FS+2,) were not different from FS- individuals. LH-RH PMT was significantly greater than zero in FS- participants, almost equal to zero in FS+1 participants, and greater than zero in FS+2 participants exhibiting greater asymmetry than that in FS- participants. These results suggest a genetic inheritance of direction and degree of handedness, being a a X-linked trait originating from mother's genotype. It was suggested that fluctuating asymmetries may reflect interactions between stochastic resonance phenomena within right and left brains. This property of brain may genetically transmitted from mother's X chromosome; a net effect of stochastic interactions between hemispheres may result in right- or left-handedness, a predominantly unidirectional coupling creating right-handedness, in favor of left brain, and a stochastic bi-directional coupling between hemispheres would be a main trait of left-handers. This new "stochastic resonance hypothesis of cerebral laterality" concerns with stochastic fluctuations in hand-skill asymmetry and inter-hemispheric coupling through corpus callosum, and seems to be important for new developments in handedness research.