The authors report on a study carried out in the University Clinic of Gynaecology and Obstetrics in Rabat on 13 cases of anencephaly without hydramnios in which post-maturity occurred. This gives them an opportunity of pointing out: --that there is a raised level of anencephaly in Morocco: --that the male sex is more commonly affected with anencephaly associated with post-maturity. And they wish to go through: --the physiological theories that are concerned with the role of the fetus in the onset of labour: --and the screening that has become possible since ultrasound and estimation of alpha-feto-protein levels have been in use, and that these should be used systematically in all pregnant women before they deliver an infant with a central nervous system malformation.