The invention concerns a spiral exchanger, consisting of two overlapping fluid circuits, a first circuit formed by the space included between two spaced sheets (1, 2) wound on themselves and a circuit formed by the space included between the successive turns of said winding. Said exchanger is characterised in that the two sheets (1, 2) comprise, on their opposite surfaces, spacing elements, said spacing elements being arranged along the longitudinal axis of the sheets (1, 2), so that, once the sheets are wound, the spacing elements of a sheet (1) are urged to be pressed on the corresponding spacing elements of the other sheet (2), the end surface of at least one of the two pressed spacing elements is globally planar.