Craniopagus twinning is an extremely uncommon birth defect with an estimated incidence of 4-6 every 10 million births. The most complex and challenging issue is the feasibility of surgical separation, which involves not only technical but also socioethical problems and requires strict multidisciplinary cooperation between pediatricians, neuroradiologists, anesthesiologists, and plastic and neurological surgeons. The authors report a case in which separation was followed by the death of both twins and stress the importance, from the surgical and prognostic viewpoints, of the degree of vascular connections between the major dural sinuses. We propose a classification into three types according to severity.