A process for the recovery and reuse of a heavy-metal oxidation catalyst solution from a high-boiling distillation residue having a cobalt content of 1-10 g/kg of residue is disclosed. The distillation residue is obtained in the production of dimethyl terephthalate by the oxidation of mixtures containing p-xylene and/or methyl p-toluate in the liquid phase with oxygen or an oxygen-containing gas under an elevated pressure and at an elevated temperature in the presence of dissolved heavy-metal oxidation catalyst, by subsequent esterification of the oxidation product with methanol and by a distillatory separation of the esterification product into a fraction rich in methyl p-toluate, a fraction rich in dimethyl terephthalate, and the high-boiling distillation residue. The process involves the steps of effecting extraction of the heavy-metal oxidation catalyst from the high-boiling distillation residue with aqueous low-molecular aliphatic monocarboxylic acids under heating; treating the aqueous, acidic extract, which contains the heavy-metal oxidation catalyst and has a cobalt content with a strongly acidic cation exchange resin in the alkali metal form at an elevated temperature until the exchange capacity has been reached, and washing the cation exchange resin at an elevated temperature with water and regenerating the cation exchange resin at room temperature with a solution containing Na.sup.+ or K.sup.+ acetate to displace the catalyst components and to obtain an aqueous acetic acid catalyst solution containing the catalyst components.