Behavior of thermo-mechanical fatigue (TMF) failure of a single crystal Ni-base superalloy, CMSX-4, was studied and, compared with isothermal low-cycle fatigue (ILCF) of it. Strain-controlled TMF and ILCF tests of CMSX-4 were carried out under various test conditions, where the experimental variables were strain rates, strain ratio, test temperature and the range, and strain/temperature phase angle. At first it was shown from the experiments that the TMF and LCF failures associated with some noteworthy characteristics were rarely seen in the traditional pollycrystalline heat-resistant alloys. These phenomena could be explained inadequately, on the basis of the macroscopic parameters and the historical failure criteria; e.g., Manson-Coffin law and Ostergren approach. A new micromechanics model is proposed to predict the TMF and LCF lives, based on the Eshelby's theory.