A cooling device for liquid-cooled internal combustion engines, which device includes an annular radiator core or block which is traversed by the cooling air from the inside thereof toward the outside thereof, with a radial-flow fan or blower equipped with a rotor being arranged on the inside of the annular radiator core or block for axially sucking in the cooling air through an opening provided in a vehicle housing. A second annular radiator core or block for cooling the fuel for the internal combustion engine is disposed concentrically within the first-mentioned annular radiator core or block at a position downstream of the rotor, as viewed in the intake direction of the cooling air. The rotor of the radial-flow fan or blower is constructed such that a communication is provided between each vaned duct of the rotor and an annular rotor side chamber disposed within the second annular radiator core or block to effect a stream of cooling air through the second annular radiator core or block.