Adhesive composition for tapes, labels and bandages to be used at temperatures of +5° C. and lower, comprising (a) at least one block copolymer, comprising at least two terminal blocks of poly(vinyl aromatic compound) and at least one midblock of a randomly copolymerized mixture of isoprene and butadiene, optionally mixed with a diblock copolymer comprising one poly(vinyl aromatic compound) block and one randomly copolymerized mixbjre of isoprene and butadiene, and optionally mixed with a block copolymer, comprising at least one block of poly(vinyl aromatic compound) and at least one block of poly(butadiene) or poly(isoprene), (b) at least one mixed aliphaticlaromatic tackifying resin or a blend of aliphatic and aromatic tackifying resins, having an aromatic H-NIVIR content between 6 and 22%, and (c) a plasticizer in an amount of at most 25 wt %, relative to the weight of the adhesive composition; and tapes, labels and bandages comprising said adhesive compositions, applied on a substrate layer; and the use of said tapes, labels or bandages.