A process for reducing the naphthenic acidity of petroleum oils or their fractions is described, said process comprising providing a hydrocarbon feed 103/203/303 having between 0.1 and 99 wt % of emulsified/dispersed water in oil, said feed containing salts and a content of naphthenic acids measured as TAN between 0.1 and 10 mg KOH/g oil; directing the said petroleum oil feed and emulsified/dispersed water towards an energy emitter device in the microwave range and submitting said feed 103/203/303 in liquid phase, under pressure between 0.7 and 4.5 MPa at temperatures between 50.degree. C. and 350.degree. C. to the microwave radiation, applied in the range of 1 mm to 30 cm to said feed so that the presence of salts, the applied temperature and the high dielectric constant of the water droplets make that the heat is absorbed on the spot by the water and heat said water preferentially to the oil, while the naphthenic compounds at the interface between the droplets and the oil catch said heat; effecting the decomposition of the carboxylic acids responsible for the naphthenic acidity in the petroleum feed at temperatures around 320.degree. C. and generating CO.sub.2; separating with the aid of any known device 106/106'/112/117/208/208'/214/219/310/310'/316/321 any gas phase generated, water and oil; and recovering the hydrocarbon oil stream 108/113/119/210/215/221/312/317/323 having a reduced content in naphthenic acids. The process is designed to be applied to the reduction of naphthenic acids in feeds of petroleum oils and their fractions in the oil production step, in refineries or any industrial installation.