An implantable tissue connector (1； 1 a) adapted to be connected to a tubular partof living tissue (70； 80) within a patient's body (100) comprises a conduit(2) and at least one flexible sleeve (10) adapted to axially extend and closelyfit around at least part of the outer surface (6) of the conduit. The conduit isinserted into the tubular part of living tissue and the flexible sleeve placedover the tubular part of living tissue. Various alternatives are described ofhow the living tissue may be prevented form slipping off of the conduit.
