EEG, VEP and BAEP studies were performed on conjoined (craniopagus parieto-occipitalis) twins, born prematurely without any common neural tissue, but with shared venous channels and contiguous posterior poles. At thirty-three wks (CA) the EEG of one of the twins showed higher amplitudes and less quiescence, suggesting a more mature cerebrum but the same twin also showed longer latencies in the BAEP, suggesting a less mature brainstem. Sleep spindles at four and a half months frequently occurred at the same time in both of the twins, at times synchronous and at other times with a latency of onset 0.5-0.8 sec from one to the other, providing further evidence for a circulating "sleep-promoting factor". VEPs were recorded that were distinctive of each of the twins. Flash stimulation of one twin produced VEPs in the other that were characteristic, not of the stimulated twin, but of the other, suggesting that evoked responses from one area can activate non-volume conducted responses from another region characteristic of that latter region, presumably by physical contiguity alone.