This system is characterized in that it includes means (2) for acquiring a signal representative of the electrocortical activity of the patient (1), means (3) for analyzing this signal in order to extract therefrom an anesthetic depth signal, means (4, 5, 6) for tracking the value and the time-dependent evolution of this anesthetic depth signal, associated with means (4, 5, 6) for computing control signals for controlling the injection means, in order to automatically bring the anesthetic depth signal to below a predetermined value during at least one predetermined period of time, in that the means for injecting anesthesia agents comprise first means (7) for injecting a hypnotic agent, and second means (8) for injecting a morphinomimetic agent, in that the means for computing control signals for controlling the injection means comprise means for inputting by an operator a type of anesthesia induction selected from a set of induction types which differ by the initial concentration of hypnotic agent and in that the means for inputting the induction type comprise means for determining the initial concentration of hypnotic agent, with which is associated an predetermined initial concentration of morphinomimetic agent depending on the selected induction type.
