A self-adhesive permeable membrane sheet, for use in a building structure, comprising a continuous layer of an air and water vapour permeable acrylic pressure sensitive adhesive attached to one surface of a permeable membrane sheet wherein the permeable membrane sheet is: a laminated construction membrane comprising three layers of polypropylene; spunbond, microporous film and spunbond; or a laminated construction membrane comprising three layers of polypropylene; spunbond, meltblown and spunbond; and wherein, the air and water vapour permeable pressure sensitive adhesive mixture used to form the adhesive layer comprises, before drying or curing: an acrylic pressure sensitive adhesive as base compound: Acrylic ester copolymer (39%) Hydrogenated rhodine ester resin (10%) ethyl acetate (50%) Vinyl acetate (1%); an air permeable agent: Water-absorbent resin (1%) Polypropylene glycol (1%) Water (98%); a cross-linking agent: Modified polyisocyanate (20-25%) Silicon dioxide(5-10%) Toluene (50-55%) ethyl acetate (15-20%); and polypropylene glycol; wherein the ratio of these components in the adhesive mixture by weight is in the range of: acrylic pressure sensitive adhesive 100: air permeable agent 10 to 40: cross-linking agent 1 to 5: polypropylene glycol 1 to 5. a laminated construction membrane comprising three layers of polypropylene; spunbond, microporous film and spunbond; or a laminated construction membrane comprising three layers of polypropylene; spunbond, meltblown and spunbond; and wherein, the air and water vapour permeable pressure sensitive adhesive mixture used to form the adhesive layer comprises, before drying or curing: an acrylic pressure sensitive adhesive as base compound: Acrylic ester copolymer (39%) Hydrogenated rhodine ester resin (10%) ethyl acetate (50%) Vinyl acetate (1%); an air permeable agent: Water-absorbent resin (1%) Polypropylene glycol (1%) Water (98%); a cross-linking agent: Modified polyisocyanate (20-25%) Silicon dioxide(5-10%) Toluene (50-55%) ethyl acetate (15-20%); and polypropylene glycol; wherein the ratio of these components in the adhesive mixture by weight is in the range of: acrylic pressure sensitive adhesive 100: air permeable agent 10 to 40: cross-linking agent 1 to 5: polypropylene glycol 1 to 5. an acrylic pressure sensitive adhesive as base compound: Acrylic ester copolymer (39%) Hydrogenated rhodine ester resin (10%) ethyl acetate (50%) Vinyl acetate (1%); Acrylic ester copolymer (39%) Hydrogenated rhodine ester resin (10%) ethyl acetate (50%) Vinyl acetate (1%); an air permeable agent: Water-absorbent resin (1%) Polypropylene glycol (1%) Water (98%); Water-absorbent resin (1%) Polypropylene glycol (1%) Water (98%); a cross-linking agent: Modified polyisocyanate (20-25%) Silicon dioxide(5-10%) Toluene (50-55%) ethyl acetate (15-20%); and polypropylene glycol; Modified polyisocyanate (20-25%) Silicon dioxide(5-10%) Toluene (50-55%) ethyl acetate (15-20%); and polypropylene glycol; wherein the ratio of these components in the adhesive mixture by weight is in the range of: acrylic pressure sensitive adhesive 100: air permeable agent 10 to 40: cross-linking agent 1 to 5: polypropylene glycol 1 to 5. acrylic pressure sensitive adhesive 100: air permeable agent 10 to 40: cross-linking agent 1 to 5: polypropylene glycol 1 to 5.