Abstract: A process for dyeing textile fibers employs a colorant medium comprising a disperse dye and an aqueous dispersion of a copolymer selected from vinyl ester-based copolymers, alkyl acrylate copolymers, alkyl methacrylate copolymers and mixtures thereof. The textile fibers are passed through at least one dye bath containing the colorant medium to deposit the colorant medium at least on the surface of the fibers. The fibers with the colorant medium deposited thereon are then passed between padding rollers to distribute the colorant medium through the fibers, whereafter the fibers are heated to cure the copolymer and bond the disperse dye to the fibers.