A process for producing carboxylic acid anhydrides by the carbonylation reaction of a carboxylic acid ester, derived from an alcohol and a carboxylic acid, with carbon monoxide containing a small amount of hydrogen in a liquid reaction medium in the presence of a Group VIII B catalyst to produce a carboxylic acid anhydride. The reaction medium comprises the Group VIII B catalyst, an organic halide, the carboxylic acid ester, an alkali metal salt, the carboxylic acid anhydride, the carboxylic acid, and at least one ionic liquid consisting of a cation and an anion where the cation of the ionic liquid has a nitrogen-containing heterocyclic structure. The ionic liquid has at least one of the following structural forms: The reaction rate of the carbonylation reaction is increased by the use of the specified ionic liquid promoters.