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The effect of minimum stress on the fatigue life has been assessed for an angle-plied nylon cord-reinforced elastomer composite which represents the bias aircraft tire carcass. The S-N curves were established under constant minimum stress rather than constant R-ratio. In this manner, all data points in each S-N curve could be associated with the same level of creep stress. Composite laminate specimens exhibited a normal failure sequence of fiber-matrix debonding developing into the delamination under cyclic tension. A trend of longer fatigue life of the composite was clearly observed at a given stress amplitude with a higher level of minimum stress. The use of a higher level of minimum stress also caused the increase of the fatigue endurance limit of the composite. The trend of longer fatigue life with a higher level of minimum stress stems from the fact that the stress and strain are not linearly related to each other.