Glycerol and aliphatic nitriles are simultaneously produced by treating liquid glycerides with gaseous ammonia at a rate of at least 200 liters of ammonia per kilogram of glyceride per hour at temperatures of from 220 DEG to 300 DEG C. in the presence of metal salts of carboxylic or sulfonic acids as catalysts and subjecting the product mixture to a phase separation into a nitrile phase and a glycerol/water phase. Preferred starting materials are vegetable and animal fats and oils.