In agonistic interactions a preference to view the opponent with the left eye before attacking has been shown in a number of vertebrate species. This and other directional biases in populations appear to be beneficial in social behaviour. For example, lateralized chicks form more stable social hierarchies than do non-lateralized ones. Recent discovery of lateralized brain function in invertebrate species has led to investigation of left-right asymmetries in social bees (honeybees and stingless bees). As in honeybees, the more primitive Australian stingless bees (3 species tested) show a clear preference to recall olfactory memory when using their right antenna but only in the first hour or so after training. By 5 hours after training, recall of the memory is no longer possible with the right antenna but now the left antenna is used. Antennal lateralities in social behaviour will be reported. Approaches and physical contacts were scored in dyads of stingless bees (Tetragonula carbonaria): dyads in which both bees had only their right antennae (RA+RA) made many more contacts than dyads in which both bees had only their left antennae (LA+LA). In dyads of LA+RA, it was found, unexpectedly, that the LA bee approached and often attacked (by biting) the RA bee much more often than vice versa. The low number of contacts in LA+LA dyads must be due to mutual avoidance, perhaps due to release of a pheromone that inhibits contact. Using a right antenna facilitates friendly social behaviour (e.g. proboscis extension and trophyllaxis), which is appropriate between hive mates, whereas using a left antenna leads to inappropriate social behaviour between hive mates. Via such left-right asymmetries, intact bees (and other species) may compute behaviour directed towards friend and foe.