A hydrocarbon partial oxidation process for obtaining gaseous mixtures comprising hydrogen and carbon monoxide is carried out through a burner (10) comprising a mixing chamber (12) that has an inner side wall (12a) extending between at least one inlet opening (23, 23a) and an outlet opening (24), independent gaseous flows of hydrocarbons and oxygen, respectively, being continuously fed into said mixing chamber (12) to form a gaseous mixture advancing towards said outlet opening (24) to be fed into a combustion chamber (14) of the gaseous mixture itself, into said mixing chamber (12) and substantially in contact with the inner side wall (12a) thereof, a flow of an inert fluid is also fed in equicurrent to said gaseous mixture, with formation of a respective annular flow of inert fluid, enveloping said gaseous mixture from which it is substantially separated by a respective inner limit layer, said annular flow of inert fluid having, at said limit layer, an advancing speed at least equal to the speed of propagation of the flame in said gaseous mixture.