Abstract: The invention relates to pipe connections satisfying hygienic demands, comprising two members which can be screwed together and a seal ring of plastically or elastically deformable material lying therebetween, and the object of the invention is to prevent the seal ring from being carried along and being displaced during tightening resulting in formation of nooks that might give rise to bacterial growth, cleaning problems and risks of contamination. According to the invention this object is achieved in that a first member has a first bore and a larger diameter second bore connected thereby by a Z-shaped transition, while a second member has an oblique end surface, a cross-sectionally triangular interspace being formed between the oblique end surface and a shoulder of the transition to receive the seal ring and to be filled out practically completely by the seal ring when the members are screwed together, and the seal ring may even protrude to some extent into the through hole.