Connection device for a secondary pipeline in combination with a transverse opening in a main pipeline, in a shaft, or in a wall, comprising: the main pipeline with the transverse opening, the shaft with the opening or the wall with the opening, a relatively soft elastomer insert in the form of a hollow plug, the outside of which insert is adapted to the transverse opening, and the inside of which has a screw region into which a connection piece can be screwed, and a relatively harder connection piece, which has an engagement end, a central part with an external thread, a receiving section and a drive end, characterised in that the inside of the elastomer insert and the outside of the central part of the connection piece are each designed as cylinder jacket surfaces such that the connection piece can be screwed into the elastomer insert, wherein when the connection device is fitted, first the connection piece is screwed into the elastomer insert up to a first screw-in position without the end section of the elastomer insert being displaced in the direction of the receiving section of the connection piece, wherein the end section of the elastomer insert ends flush with the inner surface of the main pipeline, the shaft or the wall in the area of the transverse opening in this state in the first screw-in position, and then the connection piece is screwed into the elastomer insert up to a second screw-in position, whereby the end section of the elastomer insert is displaced in the direction of the receiving section of the connection piece so that the elastomer insert is pressed at least in sections against the central part of the connection piece and against the soffit surface of the transverse opening in the main pipeline, in the shaft or in the wall. the main pipeline with the transverse opening, the shaft with the opening or the wall with the opening, a relatively soft elastomer insert in the form of a hollow plug, the outside of which insert is adapted to the transverse opening, and the inside of which has a screw region into which a connection piece can be screwed, and a relatively harder connection piece, which has an engagement end, a central part with an external thread, a receiving section and a drive end, characterised in that the inside of the elastomer insert and the outside of the central part of the connection piece are each designed as cylinder jacket surfaces such that the connection piece can be screwed into the elastomer insert, wherein when the connection device is fitted, first the connection piece is screwed into the elastomer insert up to a first screw-in position without the end section of the elastomer insert being displaced in the direction of the receiving section of the connection piece, wherein the end section of the elastomer insert ends flush with the inner surface of the main pipeline, the shaft or the wall in the area of the transverse opening in this state in the first screw-in position, and then the connection piece is screwed into the elastomer insert up to a second screw-in position, whereby the end section of the elastomer insert is displaced in the direction of the receiving section of the connection piece so that the elastomer insert is pressed at least in sections against the central part of the connection piece and against the soffit surface of the transverse opening in the main pipeline, in the shaft or in the wall.