A method and apparatus for processing a printing ink containing inhibitors and oligomers in a printing unit of a rotary printing machine in which the drying times of the printing ink on the printing material is shortened and the printing quality improved. In the illustrated embodiments, the printing unit includes two cylinders that form a press nip in which the printing ink is applied to passing printing material, and a catalyst mixture is applied to the printing material either by one of the cylinders or through an applicator device downstream of said press nip. A heating device is located in the conveying direction immediately downstream of the press nip or the applicator device.