The present invention relates to an apparatus for welding tube segments to a tubular shaped body, and to a laser welding method for connecting a tube segment to a tubular shaped body, in which the tube wall of the tube segment is constructed from at least two material layers that differ from each other, and one of these layers contains, at least portionally, an absorber for laser radiation, comprising the steps of provision of a PVC-free tube segment and a tubular shaped body, positive insertion of tube segment and tubular shaped body into one another with the result that surface regions of the tube segment and of the tubular shaped body overlap, irradiation of the overlapping surface regions with laser radiation of defined wavelength, wherein it is unnecessary, in the case of the laser welding method, to move either the joint partners or parts of the apparatus.