Endoluminal sleeve device (1) for internally lining a section of the GI tract, comprising a sleeve (2) configured for deployment inside a GI tract, the sleeve (2) having walls of a flexible material defining a sleeve lumen (3), a proximal end (4) defining a proximal lumen opening (5), and a distal end (6) defining a distal lumen opening (7), a tubular anchoring portion (8) forming said proximal lumen end (4) and defining anchoring seats (9) delimited each one by an annular collar (11) forming an opening through which adjacent tissue portions (12) can be pulled into the anchoring seats (9), expansion means adapted to act on the tissue portions (12) arranged in the anchoring seats (9) such that the tissue portions (12) expand to a dimension greater than the opening of the annular collar (11).