Aliphatic anhydrides such as the anhydrides of acetic, propionic, and alkoxy-fatty acids are produced by thermal decomposition of the corresponding acids in presence of catalysts comprising a phosphoric acid combined with a plurality of metals at least one of which is at least as electronegative as barium. The metal may be present as basic or acid radicals. A large number of double ortho, meta and pyrophosphates are mentioned, including alkalialkaline earth phosphates, alkali and alkaline earth-aluminium phosphates, purpureo and luteo potassium vanadium phosphates, potassium-antimony, barium-aluminium, calcium and copper phosphotungstates, barium, nickel and cobalt phospho-molybdates and magnesium-nickel, zinc-nickel and zinc-cobalt phosphates. By heating some of these compounds, especially mono- or di-metaphosphates, complex polymetaphosphates may be made. The treatment of the acid vapour may be effected by passing it through liquid or molten baths consisting of or containing the catalysts, and salts or other substances of low melting-point may be used to dissolve or suspend the catalysts. Suitable substances of this kind are mixtures of sodium and potassium chlorides or of calcium and magnesium or barium chlorides, or metals, such as lead, or tellurium, or alloys thereof. Or the acid vapour may be passed through tubes containing the catalysts, which may be supported upon carriers or filling materials, or in admixture with other catalysts for the reaction. Or the liquid acids containing the catalysts may be sprayed into a hot reaction zone. The acids may be preheated to or near the reaction temperature. The anhydride may be separated from the reaction vapour by the processes of Specifications 256,663, 279,916, 289,972, 298,667, 303,772 or 310,863, [all in Class 2 (iii), Dyes &c.]. In examples: (1) acetic acid vapour is preheated to 500 DEG C. and passed through molten sodium and potassium chlorides containing potassium barium tetrametaphosphate at 700 DEG C.; (2) propionic acid vapour preheated to 530 DEG C., is passed over a catalyst prepared by impregnating pumice with a solution of sodium tungstate and disodium phosphate neutralized with acetic acid, and then treating the mass with a solution of barium chloride, and if desired washing to remove sodium chloride; (3) nickel phosphomolybdate, prepared by treating nickel phosphate with molybdic oxide is first heated at 200 DEG C. and is suspended in glacial acetic acid which is preheated under 10 atmospheres pressure at 200 DEG C. and sprayed into a copper-lined reaction chamber at 700 DEG C.ALSO:Aliphatic anhydrides, such as the anhydrides of acetic, propionic, and alkoxy-fatty acids are produced by thermal decomposition of the corresponding acids in presence of catalysts comprising a phosphoric acid combined with a plurality of metals at least one of which is at least as electronegative as barium. The metal may be present as basic or acid radicals. A large number of double ortho, meta and pyrophosphates are mentioned, including alkali-alkaline earth phosphates, alkali and alkaline earth-aluminium phosphates, purpureo and luteo potassium vanadium phosphates, potassium-antimony, barium-aluminium, calcium and copper phosphotungstates, barium, nickel and cobalt phospho-molyddates and magnesium nickel, zinc-nickel and zinc-cobalt phosphates. By heating some of these compounds, especially mono- or di-metaphosphates, complex polymetaphosphates may be made. The treatment of the acid vapour may be effected by passing it through liquid or molten baths consisting of or containing the catalysts, and salts or other substances of low melting point may be used to dissolve or suspend the catalyst. Suitable substances of this kind are mixtures of sodium and potassium chlorides or of calcium and magnesium or barium chlorides, or metals such as lead, or tellurium, or alloys thereof. Or the acid vapour may be passed through tubes containing the catalysts, which may be supported upon carriers or filling materials, or in admixture with other catalysts for the reaction. Or the liquid acids containing the catalysts may be sprayed into a hot reaction zone. The acids may be preheated to or near the reaction temperature. The anhydride may be separated from the reaction vapour by the processes of Specifications 256,663, 279,916, 289,972, 298,667, 303,772, or 310,863, [all in Class 2 (iii), Dyes &c.]. In examples (1) Acetic acid vapour is preheated to 500 DEG C. and passed through molten sodium and potassium chlorides containing potassium barium tetrametaphosphate at 700 DEG C.; (2) propionic acid vapour, preheated to 550 DEG C. is passed over a catalyst prepared by impregnating pumice with a solution of sodium tungstate and disodium phosphate neutralized with acetic acid, and then treating the mass with a solution of barium chloride, and if desired washing to remove sodium chloride; (3) nickel phosphomolybdate, prepared by treating nickel phosphate with molybdic oxide is first heated at 200 DEG C. and is suspended in glacial acetic acid which is preheated under 10 atmospheres pressure at 200 DEG C. and sprayed into a copper-lined reaction chamber at 700 DEG C.