Under cyclic loadings, structures can show different types of asymptotic behaviour: elastic shakedown when the asymptotic answer is purely elastic, cyclic plasticity when plastic deformations become periodic and ratchetting, plastic deformations will then accumulate and lead to the ruin of the structure. For industrial components, elastic shakedown is related to high cycle fatigue, while cyclic plasticity and ratchetting mean low cycle fatigue, but ratchetting must be prevented since it could drastically limits the lifetime of the structure. In the automotive industry, cold parts like suspension systems often present elastic shakedown whereas hot parts like exhaust systems and cylinder heads are subjected to thermomechanical loadings and often exhibit cyclic plasticity. To evaluate the lifetime of components, one can follow the evolution of a damage variable or use a fatigue criterion that assesses the lifetime of a structure from macroscopic thermomechanical quantities evaluated on the stabilized cycle. Ambrico and Begley suggested a method to identify the different types of asymptotic behaviour in the case of fretting. In this study, we propose slightly different definitions of the cyclic part and of the ratchetting part of the deformation. The ratchetting part of the deformation er(t) is built for all instants t, taking account of the whole evolution of the plastic deformation during the cycle. Then a new definition of the amplitude of the cyclic plastic deformation during cycle k, Dec(k) is given. This definition takes into account multiaxial loadings and corresponds to the difference between two deformation states really reached during the cycle. This method is adapted to thermo-mechanical loadings with a material which mechanical characteristics depend on temperature. Finally, an application example is given on an exhaust manifold subjected to a classical thermomechanical fatigue test