The oxygenator of organic fluids comprises: a container body having a longitudinal axis; a first inlet opening for the oxygen and a second outlet opening for an exhaust gas obtained in the container body; a third inlet opening for an organic fluid to be oxygenated and a fourth outlet opening for oxygenated organic fluid obtained in the container body; an oxygenation chamber of the fluid to be oxygenated that is defined inside the container body; a distribution pre-chamber of the fluid to be oxygenated fitted between the third inlet opening and the oxygenation chamber; a mass of capillary fibers that are impermeable to liquids and porous to gasses, designed to be lapped by the organic fluid and arranged inside the oxygenation chamber according with a common parallel direction; dynamic distribution means supported in the distribution pre-chamber by support means.