To increase efficiency, mechanical engineering structures are pushed to operate under high levels of loads and temperature. Thus, they often exceed the elastic limit and develop time independent inelastic plastic strains. Also, in high temperature environment the development of time dependent inelastic creep strains is inevitable. When the loads are cyclic, with inelasticity present, the question of the assessment of the long-term strength of a structure under the continuous application of cycles can be answered by time stepping finite element procedures which follow the complete time history analysis from the very first cycle. However, a big number of cycles must be processed to reach the asymptotic long-term state. This makes the procedure, especially with creep effects present, extremely costly, as very small time steps are needed to maintain convergence. A better approach is offered by direct numerical methods that seek this asymptotic state right from the beginning of the calculations. The residual stress decomposition method (RSDM) is a successful direct method which has been developed to predict creep or plasticity asymptotic states. In the present work, the method is extended to include the combined effects of creep and plasticity. An implicit numerical scheme is presented so that convergence within a few iterations is guaranteed. The procedure can identify what kind of plastic cyclic states under creep effects is expected. At the same time, it is possible to identify the plastic-creep boundaries. A numerical example of application, under different cases of loading, underlying all the features of the procedure is presented.