A coupling for vacuum-insulated pipe or hose lines provided for conducting one or more cryogenic media, in which a single- or multi-core coupler plug and corresponding coupler socket each have a ball valve provided with a through hole and a locking sleeve coupled to rotate its respective ball valve when the sleeve is axially displaced. When the coupler plug and coupler socket are brought together, the locking sleeves engage and are displaced axially, such that the ball valves are moved into open positions in which a conduit of the coupler plug may be extended through the coupler plug ball valve into the coupler socket. Such a coupler allows a docking procedure to be reliably performed in all radial angular positions between the plug side and socket side, without need for skilled operators, position sensor technology or a precision refueling robot.