[en] The concept of an elastic core near the middle of the wall at any location in a component subjected to cyclic loading in the presence of creep was introduced by the authors to obtain bounds on the creep ratcheting strains at that location. The concept was quite useful since only elastic and creep strains could occur in the elastic core. Detailed solutions were obtained for elastic-perfectly plastic cylinders subjected to internal pressure and cyclic thru-the-wall thermal stresses. The present work includes isotropic and/or kinematic hardening effects and arbitrary temperature dependence of the yield strength of the material. The application of the bounds is extended to include loading histories with severe cycles resulting in plastic ratcheting. In general the relaxation of thermal stresses may result in a net accumulation of strain. The commonly used solution for complete relaxation between cycles does not include enhanced creep effects, and the latter are significant in many design applications