To prepare acetic acid and acetic anhydride, methanol and methyl acetate are reacted under anhydrous conditions with carbon monoxide in the presence of a catalyst system containing carbonyl complexes of group VIII noble metals, methyl iodide, an alkali metal acetate or iodide, or quaternary organophosphonium or organoammonium acetate or iodide, The hot carbonylation mixture is decompressed, the evaporated components are fed to a first distillation zone, and the catalyst solution which remains is fed back to the reaction zone. In the first distillation zone, the volatile carbonylation products are subjected to fractional distillation; the low-boiling methyl iodide and methyl acetate pass back into the reaction zone, and the bottom product produced is a mixture of acetic acid and acetic anhydride, which is split into the pure components in a second distillation zone and a third distillation zone.