The results of investigation of the dependence of fatigue strength and endurance of rods from the fibrous composite materials (glass-fiber-reinforced plastics and bazaltoplastics) on the regimes of load are given. The results of tests are analyzed from the positions of contemporary concepts about the mechanisms of the accumulation of damages with the changing loads. It is shown that the traditional explanation of the special features of the behavior of polymeric materials with a cyclic variation in the loads does not make it possible to satisfactorily explain the fatigue behavior of composite rods. The explanation of the obtained results from the positions of hypothesis about the mechano-fluctuation mechanism of the accumulation of damages is more acceptable. Hypothesis is based on the acknowledgement of that fact that the process of the accumulation of damages and the number of cycles before the destruction with the prolonged periodically changing loads in essence are determined by the work, perfected on the material of model in the half cycle of load. In the article the fixed regular (close to the harmonic) regime of load change is examined.