System for washing and sterilizing endoscopes provided with multiple channels held by a sheath, comprising a machine connected by means of multiple connectors provided with safety valves to at least one case with hermetic closure into which the endoscope is positioned, in which each of the channels of the endoscope is connected by means of a connector, the inner space of the case is connected to at least one additional connector, in such a way as to inject the washing and sterilization liquids and/or the gases for emptying the channels or drying, into each of the channels of the endoscope and into the space of the case, in which the case is also provided with an outlet connector for system circulation, in which the case is detached after the working cycle of the machine and its inner space remains in sterile conditions.