Service time and the strength of high-stressed threaded connections under cyclic nonlinear stress-strain conditions are determined by the behavior of the fatigue crack's initiation and propagation stages in local stress-strain concentration areas of threaded components. The ultimate states and failure criterion of cracked bolts/studs have been determined by analysis of the parameters of linear and nonlinear deformation and fracture mechanics. Evaluation of the number of cycles of fatigue crack initiation Nc and the number of cycles to final failure Nf for different design joints required an all-round consideration of cyclic nonelastic (nonlinear) stress-strain behavior. It also needed the further study of the influence of the conditions of cyclic, mechanical, and thermal loadings, as well as assembly and manufacturing based on the theoretical stress concentration factor Kt, (elastic deformation), stress Kσ, and strain Kϵ (nonelastic deformation) factors' values in the mated-loaded (engaged) and nonloaded (free) thread turns. The analysis indicated a linear relation between critical value hmax of the fatigue crack's depth and the cycle amplitude's stress σa, as well as a correlation with the limiting value of the stress (strain) intensity factor. The remaining strength and fatigue life of the cracked threaded components are evaluated taking into consideration the values of the current thresholds and the limiting stress and strain intensity factor. The conditions of their applicability depend on the applicability of linear (elastic) or nonlinear (elastic-plastic) fracture mechanics criteria.