A polyurethane adhesive composed of a first and a second component, wherein - the first component contains a) at least one triol A1 having a molecular weight in the range of 1,000 to 10,000 g/mol, b) at least one diol A2 having two primary hydroxyl groups and a molecular weight in the range of 60 to 150 g/mol, c) at least one alkoxylated aromatic diol A3 having a molecular weight in the range of 300 to 1,000 g/mol, and d) at least one aliphatic polyamine A4 having a molecular weight in the range of 60 to 500 g/mol, where the aliphatic polyamine A4 is an amine having two or three aliphatic amino groups, selected from: - aliphatic, cycloaliphatic or arylaliphatic primary diamines, - aliphatic primary diamines containing ether groups, and - polyoxyalkylenetriamines which are products from the amination of polyoxyalkylenetriols; and - the second component contains e) at least one polyisocyanate B1 and f) at least one polyurethane polymer B2 having isocyanate groups; - wherein the triol A1, the diol A2 and the alkoxylated aromatic diol A3 are present in such an amount that g) the weight ratio A1 /( A2 + A3) ≤ 10, and h) the weight ratio A1 / A2 ≤ 15. - the first component contains a) at least one triol A1 having a molecular weight in the range of 1,000 to 10,000 g/mol, b) at least one diol A2 having two primary hydroxyl groups and a molecular weight in the range of 60 to 150 g/mol, c) at least one alkoxylated aromatic diol A3 having a molecular weight in the range of 300 to 1,000 g/mol, and d) at least one aliphatic polyamine A4 having a molecular weight in the range of 60 to 500 g/mol, where the aliphatic polyamine A4 is an amine having two or three aliphatic amino groups, selected from: - aliphatic, cycloaliphatic or arylaliphatic primary diamines, - aliphatic primary diamines containing ether groups, and - polyoxyalkylenetriamines which are products from the amination of polyoxyalkylenetriols; and a) at least one triol A1 having a molecular weight in the range of 1,000 to 10,000 g/mol, b) at least one diol A2 having two primary hydroxyl groups and a molecular weight in the range of 60 to 150 g/mol, c) at least one alkoxylated aromatic diol A3 having a molecular weight in the range of 300 to 1,000 g/mol, and d) at least one aliphatic polyamine A4 having a molecular weight in the range of 60 to 500 g/mol, where the aliphatic polyamine A4 is an amine having two or three aliphatic amino groups, selected from: - aliphatic, cycloaliphatic or arylaliphatic primary diamines, - aliphatic primary diamines containing ether groups, and - polyoxyalkylenetriamines which are products from the amination of polyoxyalkylenetriols; and - aliphatic, cycloaliphatic or arylaliphatic primary diamines, - aliphatic primary diamines containing ether groups, and - polyoxyalkylenetriamines which are products from the amination of polyoxyalkylenetriols; and - the second component contains e) at least one polyisocyanate B1 and f) at least one polyurethane polymer B2 having isocyanate groups; e) at least one polyisocyanate B1 and f) at least one polyurethane polymer B2 having isocyanate groups; - wherein the triol A1, the diol A2 and the alkoxylated aromatic diol A3 are present in such an amount that g) the weight ratio A1 /( A2 + A3) ≤ 10, and h) the weight ratio A1 / A2 ≤ 15. g) the weight ratio A1 /( A2 + A3) ≤ 10, and h) the weight ratio A1 / A2 ≤ 15.