A connecting device for pipe or hose lines with a threaded connection body having a bore for passing through a medium flowing through the pipe or hose line and with a pipe-like end piece which can be plugged into a receptacle constructed at the front end of the threaded connection body and can be fixed therein by means of a union nut which has an internal thread, which can be screwed onto an external thread applied on the outer circumference of the threaded connection body, and is arranged rotatably between a release position and an installed position, wherein the receptacle of the threaded connection body is constructed in the form of an expanding cone and the circumferential surface of the end piece engaging into the receptacle has a conical shape corresponding to the receiving cone constructed on the threaded connection body and tapering to the end of the end piece, wherein the circumferential surface of the threaded connection body carrying the external thread has a course in the direction of its front end which is inclined oppositely to the cone of the receptacle and the union nut has a course complementary thereto on its surface carrying the internal thread, and external thread and internal thread are constructed as tapered threads such that in the case of installed connecting device, radial force exerted by the conical end piece onto the receiving cone constructed in the threaded connection body is directed oppositely to a radial force emanating from the tapered thread with the union nut screwed on.