Abstract: In an exhaustion process for dyeing unmodified or acid-modified polyester fibers, the fibers are introduced into a dye bath comprising a chlorinated hydrocarbon solvent, a water-insoluble salt of a cationic dye and a C.sub.6-13 alkyl sulfosuccinate anion, from 0.05 to 1.0% based on the total weight of the dyebath of at least one low molecular weight carboxylic acid, a solvent-soluble quaternary ammonium salt of an arylsulfonic acid and optionally additional processing assistants, after which the cationic dye salt is exhausted onto the unmodified or acid-modified polyester by heating the dyebath at a temperature of from 110.degree. to 170.degree. C for from 0.5 to 3 hours, with the proviso that, in the case of the acid-modified polyester fibers, from 0.01 to 0.10% based on the total weight of the dyebath of water must also be present in the dyebath. Good to excellent penetration of and buildup on the polyester fibers are obtained.