High oxygen affinity hemoglobins are responsible for rare and heterogeneous autosomic dominant genetic diseases. They cause pure erythrocytosis, sometimes accountable for hyperviscosity and thrombosis, or hemolysis. Differential diagnoses must be first ruled out. The diagnosis is based on the identification of a decreased P50, and their possible characterization by cation exchange-high performance liquid chromatography and capillary electrophoresis. Finally, genetic studies of the responsible globin chain gene will confirm the mutation. The prognosis mainly relies on the P50 decrease rate and on the hemoglobin cooperativity impairment. Disease management should be personalized, and it should primarily depend on smoking cessation and physical activity. Phlebotomy and platelet aggregation inhibitors’ prescriptions can be discussed. There is no contraindication to flights, high-altitude conditions, or pregnancy. Nevertheless, blood donation must be prohibited.