The invention relates to a device for the sealing connection of a pressure hose (2) with a grip element (4) of a surgical instrument (30, said device comprising at least one sealing element (8) that, in assembled state, is interposed between the grip element (4) and the pressure hose (2) in a connecting region (10) so as to create a seal, whereby a support element (12) is provided, said support element being arranged in the connecting region (10) in the interior (14) of the pressure hose (2) in such a manner that the sealing element (8) is clamped, or can be clamped, between the support element (12) and the pressure hose (2) on one side and the grip element (4) on the other side. In addition, the invention also relates to a handle for a surgical device, in particular a cryogenic surgical instrument, comprising a grip element (4) for holding the surgical instrument (30), and comprising at least one pressure hose (2) that is connected, or can be connected, with the grip element (4) via a device (1) of the aforementioned type.