1. Preface When the metallic materials were broken down due to fatigue under repeated stresses, it was previously published partially that the repeating speeds had influences upon the fatigue-curves, especially the endurance limits. But they were not investigated systematically. The causes lay, it was though, in the fact that no reliable high speed fatigue testing machine was available. In this research, some carbon steels from 0.07% to 0.6% carbon has been studied under the new Nishihara type high speed fatigue testing machine, which was designed as satisfying the purposes, and also under the old Woler type fatigue testing machine, and some other materials were also studied. 2. Effects of the repeating speeds We have studied on the range from 5, 000 rpm to 15, 000 rpm by the new Nishihara type high speed fatigue testing machine, and studied on the range from 50 rpm to 2, 000 rpm by the old Woler type fatigue testing machine. It was imperfectly known that the endurance limits were rising as the repeating speeds were rising. By this research, the facts that the endurance limits were rising as the repeating spceds were rising were confirmed, and these rates of the rising are different according to the contents of carbons or the internal crystal systems or the results of the heat treatment. When we consider all states of fatigue curve at the high stresses, the materials are fatigued sooner in the cases of repitition of high speed than of low speed, i. e. at the high stresses, the fatigue strengths are lower than at the low stresses, at the high speed repitition. But at the endurance limits, or at the lower stresses near such limits, the materials are fatigued sooner in the case of repitition of low speed than of high speed. As the cause that the fatigue strength is varied by such variations of the repeating speeds, we consider 2 causes. At the high stresses the facts that the fatigue strengths at the high speed repetitions are lower than at the low speed repetition, are considered as the next. The heat quantity which is accumlated in the material in unit time is much larger at high speed repetition than at lower speed repetition, and then the temperature of the material rises and the material is softened. So the strength becomes smaller. At the low stress near the endurance limits, the rising of temperature of the material is very much smaller, but on the contrary, the variations of the internal crystal system are larger at low speed repetition than at high speed repetition, so that the material at low speed repetition is fatigued sooner than at high speed repetition. 3. Conclusion To save the testing time of fatigue test, we perform the fatigue test under high speed repeating stresses. But by such a method, the phenomena, that the endurance limits were varied by the repeating speed, were discovered, and the facts that according to the internal crystal system of material, the rate of influences was different, was also discovered. we now believe that we must study another materials, ana discuss the effects of the repeating speed that influences the fatigue strength.