An apparatus (10) for extracorporeal hematic treatment is described. The apparatus comprises an oxygenator (15) provided with a microporous membrane in the form of hollow capillaries, means (33) for feeding a flow of blood to the oxygenator at a first pressure value, and means for feeding a flow of working gas to the oxygenator at a first pressure value. Advantageously, the apparatus comprises a control unit (17) programmed to produce at least one pressure peak in the flow of working gas fed to the oxygenator, with the provision that the maximum value of the pressure peak caused in the flow of working gas is lower than the pressure value of the flow of blood in the oxygenator or coming out therefrom. A process for maintaining the lumina of the hollow capillaries of the microporous membrane of the oxygenator free from condensation is also described.
