The invention relates to a composition for dyeing keratin fibers, in particular human keratin fibers such as the hair, comprising at least one cationic direct dye of given formula and at least one thickening polymer chosen from nonionic guar gums, biopolysaccharide gums of microbial origin, gums derived from plant exudates, pectins, alginates, starches, and carboxyalkylcelluloses. The invention also relates to the dyeing processes and dyeing devices using the composition.