A heat exchanger has walls of plastic foil for demarcation between two groups of slot-formed channels for a first and a second fluid respectively. In order to hold the walls (10, 14, 15) of the channels at a mutual distance, in each channel there is disposed a continuous distance-holding layer (7, 9) of metal or plastic material which is configured as projections, ribs or another surface structure, so that a fluid can flow through the channel (6, 8) while the channel's walls (10, 14, 15) lie up against the distance-holding layer (7, 9). The structure formed by the walls (10, 14, 15) and the distance-holding layers (7, 9) is built into a compression casing (11, 12, 13, 16, 17), so that an over-pressure in the channels (6, 8) is transferred to the compression casing (11, 12, 13, 16, 17). The walls (10, 14, 15) can be wound in spiral form. The heat exchanger can be built up of a foil tube, in which is placed an inner distance-holding layer (7), and which is wound together with an outer distance-holding layer (9) placed on the outside of the foil tube. By melting down, plane end plates (18, 19) can be formed in the ends of the heat exchanger. The distance-holding layers are of metal and/or plastic wave.