A cyclic polycarboxylic acid anhydride, a polycarboxylic acid, or a mixture of them is allowed to react with hydroxylamine or a salt thereof in an organic solvent under dewatering conditions to yield a corresponding cyclic N-hydroxyimide compound. The cyclic polycarboxylic acid anhydride can be, for example, succinic anhydride or glutaric anhydride. The polycarboxylic acid can be, for example, succinic acid, glutaric acid, or adipic acid. In this process, the reaction is preferably carried out using an organic solvent capable of undergoing azeotropy with water as all or part of a reaction solvent while removing water from the reaction system by azeotropy with the organic solvent. This process produces a cyclic N-hydroxyimide compound in a good yield from any of a cyclic polycarboxylic acid anhydride and a polycarboxylic acid.