In a heat exchanger, such as a steam generator equipping a nuclear power station, the intermediate inwardly curved parts (14c) of the U- tubes (14) grouped into a bundle forming parallel layers are maintained by antivibration bars (36a, 36b', 36c') placed between each pair of adjacent layers, these bars being interconnected outside the bundle by connecting pins (38a, 38b, 38c). To prevent the fly-off of the assembly formed by the antivibration bars and the connecting pins, at least part of the bars (36a, 36b', 36c') are placed in slots formed in an elongated structure (40) fixed to the spacing plate (34a) closest to the inwardly curved part of the tubes.
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