The disclosure provides compositions for dyeing keratin fibers, such as human keratin fibers including the hair, comprising, in a medium that is suitable for dyeing, at least one oxidation dye precursor, at least one alcohol oxidase enzyme, at least one enzyme substrate, and at least one polyurethane associative polymer. The disclosure also provides processes for dyeing keratin fibers, which comprises applying the compositions, and also to dyeing “kits.”