Abstract: A tubular coiled heat exchanger adapted for cooling or heating of various fluids in various fields of industry. The heat exchanger comprises a shell and a core around which tubes having essentially the same length are wound at least in two layers. The tubes may have grooves projecting into the tubes to intensify heat abstraction within the tubes. A member of a streamlined cross-section, such as, a wire, adapted for forming fins is wound around the tubes with a pitch of at least twice the diameter of the wire. The tubes are wound around the core so that the tops of the fins of each tube coil come alternately in contact with those of the fins and with tube surfaces of adjacent coils. The above embodiment of the heat exchanger makes it possible to vary the number of turns of the tubes when winding the tubes being set once without any distance pieces between the layers. This ensures the manufacture of a highly compact heat exchanger featuring high thermal and hydrodynamic properties.