Abstract: A knee joint endoprosthesis is provided, having a femur component to be anchored by a shaft and equipped with two gliding runners, which between them define a hollow space extending anteriorly to posteriorly and open toward the tibia, and a tibia component also to be anchored by a shaft and having two gliding surfaces on which the gliding runners of the femur component can execute rolling and gliding movement. The knee joint endoprosthesis is characterized by the tibia component being equipped with a double truncated cone, which is arranged with its main axis toward the femur and which serves as a guiding and stress reducing element. Further, a pair of guiding surfaces is constructed in the hollow space of the femur component. These surfaces are inclined at angles corresponding respectively to the angles of inclination of the two half truncated cones that form the double truncated cone. The cone surfaces of the half truncated cones are partially surrounded by and glide upon the pair of guiding surfaces.