Two-stress level cumulative fatigue damage was studied on a cross-plied E glass fiber/epoxy laminate (Scotchply type 1002). Tests were performed in fluctuating tension with the minimum value of cyclic stress equal to 5 percent of the maximum value of cyclic stress (R = 0.05). The results show that for a high-low stress cumulative damage test the Miner's sum, (n₁/N₁)+(n₂/N₂), is greater than unity and for a low-high stress test less than unity. The deviation from unity depends on the difference between the high and the low stress levels. These observations can be explained on the basis of a theory proposed here which takes into account the reduction of the tensile strength of the material due to cyclic loading. The residual strength of the composite at a given stress level has been determined as a function of number of cycles or fractional life spent. The predicted values of Miner's sum based on strength reduction curves agree qualitatively and quantitatively with the experimental values.