Chronic primary Mg deficiency is frequent. About 20% of the population consumes less than two-thirds of the RDA for Mg. Women, particularly, have low intakes. For example, in France, 23% of women and 18% of men have inadequate intakes. Mg deficiency during pregnancy can induce maternal, fetal, and pediatric consequences that might last throughout life. Studies of gestational Mg deficiency in animals show that Mg deficiency may have marked effects on parturition and postuterine involution. It has interfered with fetal growth and development, and caused morbidity from hematological effects and disturbances in temperature regulation, to teratogenic effects. Emphasis, here, is on effects of chronic clinical gestational Mg deficiency as it affects the infant. Premature labor, contributed to by uterine hyperexcitability caused by chronic maternal Mg deficiency, that can be intensified by stress, gives rise to preterm birth. If the only cause of uterine overactivity is Mg deficiency, its supplementation constitutes nontoxic tocolytic treatment, as an adjuvant treatment, that is devoid of toxicity and enhances efficacy and safety of tocolytic drugs such as beta-2 mimetics. Evidence is considered that Mg deficiency or Mg depletion can contribute to the Sudden Infant Death Syndrome (SIDS). SIDS may be a fetal consequence of maternal Mg deficiency through impaired control of Brown Adipose Tissue (BAT) thermoregulation mechanisms leading to a modified temperature set point. SIDS can result from dysthermias: hypo- or hyperthermic forms. Possibly, simple nutritional Mg supplements might be preventive. Various stresses in an infant can transform simple Mg deficiency into Mg depletion. For example, lying prone can be stressful for the baby, as can parental smoking. The role of chronopathological stress appears to be often neglected, as it constitutes a clinical form of primary hypofunction of the biological clock [with its anatomical and clinical stigma such as reduced production of melatonin (MT) and of its urinary metabolite: 6 Sulfatoxy-Melatonin (6 SMT)]. SIDS might be linked to impaired maturation of both the photoneuroendocrine system and BAT. Prophylaxis of this form of SIDS should include atoxic nutritional Mg therapy for pregnant women with total light deprivation at night for the infant. Consequences of maternal primary Mg deficiency have been inadequately studied. To determine ultimate outcomes of gestational Mg deficiency in infants, a long-term multicenter placebo-controlled prospective study should undertaken on effects of maternal nutritional Mg supplementation on lethality/morbidity in fetus, neonates, infants, children and adults, not only during pregnancy and the baby's first year, but throughout life.