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); wherein R1 and R3 are each a C1 - C2 alkyl group, R2 is a hydrogen atom, a C1 - C2 alkyl group or a C1 - C2 alkoxy group, R4 is a hydrogen atom or a C1 - C2 alkyl group, R5 is a hydroxyl group or a C1 - C2 alkoxy group, and X- is an anion. The dye compounds of the formula (I) dye acid-modified polyester fibers a bright shade and with good light fastness. The dye compounds of the Formula (I) wherein R2 is a hydrogen atom or a methoxy or ethoxy group are novel dye compounds.
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