A heat exchanger of the spiral-coil type in which, around a core tube, a sheet of thermally conductive material, e.g. metal, is coiled in a spiral to define passages between the turns of the spiral traversed by fluids to be subjected to heat exchange. According to the invention, neighboring metal sheets define flow passages between them and are sealed along the faces of the sheets and along the longitudinal edges over spaced-apart units of length so that the sections between the sheets are alternately open and closed at the longitudinal edges. The open passages at the longitudinal edges can communicate with a hood through which the fluid is distributed to or removed from a respective passage.