We report three reaction time experiments in which first names were laterally presented and subjects made discriminatory manual or vocal responses (male/female), or named the stimuli, or judged whether name pairs were of same or opposite sex. The experiments addressed the issue of whether the strength and direction of laterality effects changed with practice and/or stimulus repetition. Performance facilitation with a repeated stimulus was greater when the same rather than the opposite hemisphere received the repeated stimulus, indicating that the effects of stimulus repetition are partly hemisphere-specific. Task practice was found to be a far more important determinant of changing asymmetries than stimulus repetition; however such practice may decrease as well as increase lateral asymmetries. These effects did not extend to the situation where a task was preceded by another of quite a different nature--name before face processing, and vice versa. We conclude that sequencing and practice effects are important but complex determinants of the direction and magnitude of lateral asymmetries, indicating that lateral asymmetries are labile rather than fixed and reflect relative rather than absolute specialization in interhemispheric processing capacity.