A connector unit for connecting capillaries, for high-performance liquid chromatography includes a connector capillary, a connector housing, and an annular sealing element. The connector capillary projects through a bore of the connector housing. The annular sealing element is provided on a front end region of the connector capillary and which is composed of a plastically and/or elastically deformable material. The connector capillary has an inner shell composed of a plastically and/or elastically deformable material and an outer shell which engages around the inner shell. The inner shell has a radially outwardly extending front end region which, on its own or together with the annular sealing element can generate a seal between the front end region of the connector capillary and a bushing unit.