The invention relates to a process for preparing isocyanates and/or polyisocyanates by reacting the corresponding amines with phosgene, optionally in the presence of an inert medium, in a reactor (1), a first reactant stream comprising the amine being supplied to the reactor (1) in liquid form, and a second reactant stream comprising the phosgene being supplied to the reactor in gaseous form. The reactor is a centrifugal reactor (1) having a packing (9) which rotates about a central axis (7) in a housing (13), the first reactant stream and the second reactant stream being supplied to the rotating packing (9) such that the reactant streams are mixed due to the centrifugal force in the rotating packing (9) and are transported outward, the mixing in the rotating packing (9) resulting in reaction of the phosgene with the amine to give the corresponding isocyanate or polyisocyanate.