Twenty-four male and twenty-four female undergraduates took part in an experiment to investigate the effects of gender and familial handedness on hemispheric activation during numeric and visuospatial thinking. Each gender group was divided into twelve subjects with close left handed relatives and twelve subjects without. All subjects were overtly right handed. EEG alpha activity was recorded from left and right occipital and parietal regions with respect to mastoid references while the subjects performed numeric tasks with eyes open and with eyes closed, a face-recognition and a tactile-discrimination (figural-unification) task. EEG alpha power was quantified during these conditions and during relaxed wakefulness with eyes open and eyes closed. Relative activation, (suppression of alpha activity from rest) of left and right parietal regions during numeric and spatial tasks was found to depend upon gender and familial handedness. Males, not females, tended to switch from left hemisphere activation during face recognition. Irrespective of gender and to some extent of task, a tendency towards greater activation of the right hemisphere was associated with the possession of left handers among close relatives.