A process for dyeing acid-modified polyester fibers comprising contacting the fibers with a dye bath containing a thiazoleazo-type cationic dye of the formula (I), ##SPC1##wherein R.sub.1 and R.sub.2 each is a methyl group or an ethyl group; A and B each is a benzene nucleus which can be substituted with a methyl group, an ethyl group, a methoxy group or an ethoxy group; and X.sup.- is an anion. The cationic dye compounds of the formula (I) dye acid-modified polyester fibers a bright blue shade and with good light fastness.