A plug unit for connecting capillary tubes includes a plug housing that has an axial borehole, a plug capillary tube that projects through the axial borehole, and a sealing element that surrounds the plug capillary tube. The front end of the plug capillary tube is sealed by an elastic and/or plastic deformation of the sealing element against the capillary tube receptacle opening of a bushing unit. A hollow cylindrical pressure piece is provided that surrounds the sealing element in an axial region facing away from the end surface of the plug capillary tube, and the pressure piece has a rearward end side that faces away from the end surface of the plug capillary tube and that can be loaded by the plug housing with an axial pressure force when the plug unit and bushing unit are connected.