A process produces a corresponding dicarboxylic acid by subjecting a cycloalkane to an oxidative cleavage reaction with oxygen in the presence of a catalyst in a liquid phase using a continuous reactor, in which a residence time .tau. (hr) satisfies the following condition: 0.1.ltoreq..tau..ltoreq.50/c, wherein c is the proportion (% by weight) of the cycloalkane to the total weight of a charged liquid. The catalyst includes, for example, cobalt compounds, manganese compounds, and mixtures of these compounds, as well as imide compounds having at least one cyclic imide skeleton.