A cross-current pipe heat-exchanger for gases, especially for a gas turbine installation, with at least one collective space for the heat-absorbing gas and a bundle of pipes adjoining a wall of the collective space and formed of a large number of individual pipes fastened in the wall and conductively connected with the collective space; the gas stream which gives off heat thereby flows transversely through the pipe bundle; a number of pipes in the pipe bundle arranged on the inlet side are constructed relatively thick-walled, at least within the area of their fastening in the wall; preferably these thick-walled pipes have a wall thickness of about 50 to 100% of the wall thickness of the wall portion forming the adjacent collective space.