Gestational surrogacy covers three different and often mixed up situations. In the first case (that of full surrogacy), the surrogate mother carries and has the baby anonymously. The child has been conceived by artificial insemination with her own oocyte and the help of the financing father, who has legally recognised the child before birth. This constitutes surrogacy motherhood practice, which was condemned by a judgment of the French Court of Cassation, in 1991. In the second case (gestational surrogacy), the mother only carries an embryo conceived in vitro by the biological parents to whom she will give back the baby when he is born. The filiation tie between the child and his parents is thereby maintained, the surrogate mother's role being limited to that of gestation. In the third case, the surrogate mother carries an embryo, the result of in vitro fertilization of the oocytes of a donor and the father's sperm. From the moment that surrogacy is not at variance with any of our fundamental rights, we cannot but wish that, with the guarantee of a rigorous frame, it might become a medical indication for IVF, in precise circumstances of female infertility.