The concept of cerebral death is universally accepted. It rests on a panel of signs which must all be present and constant, and provided this is the case no error is possible. No authentic case throwing doubt on this statement has ever been reported. It has been said that the term "coma dépassé" which we chose in 1959 could lead to confusion with the different degrees of coma and for this reason, be an obstacle to organ donation. I do not consider this a satisfactory explanation. In favour of the appellation "coma dépassé" are the originality of its first description and its use in the French medical language. It does not matter if "cerebral death" is preferred, both terms being synonymous. The individualization of "coma dépassé" and the possibility of grafting organs with success are acquisitions separated by only a few years. They have made it possible to obtain the remarkable successes known to every one, they have given medical thinking a new dimension and placed upon doctors an increased responsibility.