An implantable tissue connector (1 1a) adapted to be connected to a tubular part of living tissue (70 80) within a patients body (100) comprises a conduit (2) and at least one flexible sleeve (10) adapted to axially extend and closely fit around at least part of the outer surface (6) of the conduit. The conduit is inserted into the tubular part of living tissue and the flexible sleeve placed over the tubular part of living tissue. Various alternatives are described of how the living tissue may be prevented form slipping off of the conduit.
