A 3D extrusion print process for producing multicolored three-dimensional objects is provided. The process produces mechanically stable, multicolored 3D objects with good color definition. The process according to the invention is based on coating, upstream of the printing head, of the polymer strand used for producing the actual object, and on fixing of the coating upstream of entry of the polymer strand into the printing head. Downstream of the extrusion process in the printing head, the coating remains predominantly at the surface of the extruded strand.