This article will present some of the arguments that have been exposed about the legal acceptability in the technique of gestation of human life by surrogacy, beginning for establish the multiple denominations that have been realized and which make know this technique as: surrogacy, surrogate motherhood or substitute motherhood. Then it will determine the legal aspects involved in the transit of this technique to its accomplishment through contracts, thereby specifying the essential elements (capacity, consent, cause and lawful purpose), the content and the possible manner of gestation human life contracts by surrogacy.