An experimental program was carried out to investigate the laws of damage summation in conditions of prolonged cyclic loading with endurance. Kinetic deformation criteria of cyclic fracture at high temperatures are proposed. On the basis of the data obtained some approaches to the evaluation of prolonged cyclic strength, known from literature, are analyzed. Experiments were carried out on Cr18Ni10Ti austenitic stainless steel samples in condition of tension-compression at the temperature of 650 C. Tables of results are presented.