The influence of variable amplitude loading on fatigue crack propagation was investigated for two high purity versions of the alloy Al 2024 in sheet form, one with fine equiaxed grains, and the other with coarse elongated grains. Fatigue tests on center cracked specimens were conducted in vacuum at constant amplitude (R-ratio of 0.1) and with periodically applied single tensile overloads with an overload ratio of 1.5. The number of intermittent baseline cycles between consecutive overloads was varied (n=100 and n=10.000). Detailed fractographic investigations were carried out for the identification of changes in the fracture surfaces due to the overloads. Crack closure measurements were performed in all cases. The results revealed a strong influence of the overloads on the crack propagation rate. Whether overloads are retarding or accelerating the fatigue crack propagation depends on the crack propagation mechanism at constant amplitude loading and the number of intermittent baseline cycles. For n=100 retardation occurred for the fine grained alloy exhibiting homogeneous slip at constant amplitude while acceleration was observed for the alloy with coarse elongated grains showing pronounced slip band fracture at constant amplitude. For n=10.000, the formation of steps parallel to the direction of crack propagation by overloads is assumed to be the reason for the observed increase in fatigue crack propagation resistance resulting in retardation for both alloys compared to constant amplitude and n=100. The influence of crack closure on the overload effects was minor. This was verified by additional tests at R=0.5.