The paper presents the underlining physical concepts as well as the results of an investigation of the interaction of repeated stress cycles of variable amplitude in producing progressive (fatigue) damage. The materials investigated were 2024 aluminum alloy and 4340 aircraft steel; and the applied load spectra were based on simplified exponential distributions of gust loads and maneuver loads, as suggested by Lundberg. The fatigue tests were performed on rotating bending fatigue machines of special design, in which randomized sequences of load amplitudes, derived from the given spectra, were applied. The results of the investigation support the proposition of a quasi-linear cumulative damage rule, deviating significantly from the simple linear (so-called Miner) rule, but equally easy to apply in design. They also demonstrate the lack of design significance of the conventional endurance limit in ferrous metals.