Aromatic isocyanates are produced by reacting one or more aromatic primary amines with phosgene in the gas phase. The phosgene and primary aromatic amine(s) are reacted at a temperature above the boiling temperature of the amine(s) in a reactor having a reaction space which is essentially rotationally symmetric to the direction of flow. The flow fate, averaged over the cross-section, of the reaction mixture along the axis of the essentially rotationally symmetric reaction space in the section of the reaction space in which the conversion of the amine groups into isocyanate groups is between 4 and 80% is not more than 8 m/sec. The flow rate averaged over the cross-section of the reaction mixture along the axis of the essentially rotationally symmetric reaction space in the section of the reaction space in which the conversion of the amine groups into isocyanate groups is 4 to 80% is always below the flow rate averaged over the cross-section at the start of this section.