A counterflow cylindrical recuperative heat exchanger with multi-thread screw-like coiled heat exchanger surfaces, designed especially for ventilating devices, including inlet for one medium and outlets for a counterflow second medium, wherein one medium is fresh air and the counterflow second medium is contaminated air, wherein, if the flow directions are inversed, the medium inlets become the medium outlets and the medium outlets become the medium inlets; and an external pipe with a coaxially arranged internal pipe, between which heat exchanger surfaces are situated in screw-like shapes, wherein both ends of the recuperative heat exchanger being fitted with annular distributors for the inlets of one medium into inlet channels and outlets of the counterflow medium into outlet channels; and each annular distributor defining the inlets for one medium and the outlets for the counterflow medium, and each annular distributor is provided with external separation surfaces and internal separation surfaces for separation of the inlet channels and outlet channels of both counterflow mediums, wherein a number of external separation surfaces is equal to the number of internal separation surfaces, which is equal with number of inlet channels or outlet channels, where the inlet channels and the outlet channels are arranged side by side in an alternating manner, a plurality of inlets of the one medium are arranged in a radial way or in a semi-radial way on the end annular distributor, radially with regard to the longitudinal axis of the recuperative heat exchanger, and following up to the inlet channels arranged between the external pipe and the internal pipe for the flow of the one medium; a plurality of outlets of the counterflow second medium are directed in an axial way on the end annular distributor, and distributed radially with regard to the longitudinal axis of the recuperative heat exchanger, and following up to the outlet channels for the flow of the counterflow second medium; the heat-exchanger surfaces are mutually separated, coaxial, multithread screw-like coiled between the external pipe and the internal pipe and outline the mutually separated inlet channels and outlet channels for the flow of both counterflow mediums, and the heat-exchanger surfaces and therefore also the inlet channels and outlet channels are arranged radially around the longitudinal axis of the recuperative heat exchanger; and the profile (8, 16) of the heat exchanger surfaces features one shape, in the transverse section perpendicular to the longitudinal axis of the recuperative heat exchanger, from the group including parts of a straight line, circle, helix, involute, parabola and hyperbola wherein the heat exchanger surfaces have screw-like shapes, wherein the right-handed or left-handed helix (6, 7) of the heat-transfer surface is coiled under the pitch angle, which is greater than 0° and smaller than 90° with regard to the longitudinal axis of the recuperative heat exchanger; the heat exchanger surfaces feature a shape, outlined with external edges, consisting of external helices on the external pipes and internal helices on the internal pipe; and each annular distributor has the external separation surface and the internal separation surface in a conical shape of a truncated cone.