The present invention relates to a process for producing dyed polyester fibers (C) from a terephthalate polyester (A), at least one polyester-containing additive (B) and optionally at least one component (G). The polyester-containing additive is obtainable by condensation of the monomers of an aliphatic 1,ω-diol, of an aliphatic 1,ω-dicarboxylic acid and of an aromatic 1,ω-dicarboxylic acid. Optionally, chain extenders (V) are also used in the production of the polyester-containing additive (B). For fiber production, the components (A), (B) and optionally (G) are mixed, melted in an extruder and extruded through spinneret dies. These polyester fibers (C) are preferably used in the production of dyed textile fabrics (F).