All agreeing patients will be randomized in one of the two following groups: - 1. Induction of labor between 37+0 and 38+6 GW and within 3 day after the randomization. - 2. Expectancy until the spontaneous beginning of labor or up to 41 GW.The measurement of principal exit is the neonatal traumatism (criterion composite associating: dystocia of the shoulders, fractures osseous, paralysis/paresis of the plexus brachial or intracerebral haemorrhage).The secondary criteria are neonatal asphyxiation (arterial pH < 7.10 or Apgar < 7 to 5 minutes), the maternal traumatism (tear of 3rd or 4th degree) and the Caesarean. The long-term after-effects for the mother and her child will be also evaluated.