An implantable tissue connector (1, 1a) adapted so as to be connectable to a tubular part of living tissue within a patient's body, comprising - a conduit having at least a first end and a second end and further having an outer surface with at least one bulge extending outwardly from the conduit's outer surface in a circumferential direction of the conduit about at least a part of the conduit's circumference, - at least one blocking ring loosely fitting over the outer surface of the conduit with a clearance between the outer surface and the blocking ring for mounting said tubular part of living tissue within the clearance, said blocking ring having an inner cross sectional diameter which is smaller than or substantially identical to an outer cross sectional diameter of the at least one bulge so as to prevent the blocking ring from slipping over the bulge when said tubular part of living tissue is mounted within the clearance, - at least one flexible sleeve either mounted on or for mounting on the outer surface of the conduit such that it axially extends around at least part of said conduit and such that, when said tubular part of living tissue is pulled over one of the first and second ends (3, 4) of the conduit so as to extend over the bulge, the tubular part of living tissue can be located somewhere between the conduit and the flexible sleeve and the blocking ring can be pushed over the flexible sleeve against the bulge, - such that, when the tubular part of living tissue is being pulled off of said one end (3, 4) of the conduit, the blocking ring will be moved with the tubular part of living tissue, press the tubular part of living tissue and the flexible sleeve against the bulge, and thereby prohibit any further slippage of the tubular part of living tissue over the bulge. - a conduit having at least a first end and a second end and further having an outer surface with at least one bulge extending outwardly from the conduit's outer surface in a circumferential direction of the conduit about at least a part of the conduit's circumference, - at least one blocking ring loosely fitting over the outer surface of the conduit with a clearance between the outer surface and the blocking ring for mounting said tubular part of living tissue within the clearance, said blocking ring having an inner cross sectional diameter which is smaller than or substantially identical to an outer cross sectional diameter of the at least one bulge so as to prevent the blocking ring from slipping over the bulge when said tubular part of living tissue is mounted within the clearance, - at least one flexible sleeve either mounted on or for mounting on the outer surface of the conduit such that it axially extends around at least part of said conduit and such that, when said tubular part of living tissue is pulled over one of the first and second ends (3, 4) of the conduit so as to extend over the bulge, the tubular part of living tissue can be located somewhere between the conduit and the flexible sleeve and the blocking ring can be pushed over the flexible sleeve against the bulge, - such that, when the tubular part of living tissue is being pulled off of said one end (3, 4) of the conduit, the blocking ring will be moved with the tubular part of living tissue, press the tubular part of living tissue and the flexible sleeve against the bulge, and thereby prohibit any further slippage of the tubular part of living tissue over the bulge.