A structure subjected to thermomechanical cyclic loadings may exhibit various cyclic behaviours: perfect elasticity, elastic shakedown, plastic shakedown and ratchetting. The quantitative characterization of these different asymptotic states is addressed in this paper, in the context of the Generalized Standard Materials (GSM). Criteria are established to identify them and capture the trend line of their evolution, in the context of numerical simulation. The definitions are extended to the case of temperature dependent mechanical properties. Simple strain paths are first considered to illustrate the relevancy of the proposition. Finally, as an application, the example of an exhaust manifold subjected to a classical thermomechanical fatigue test is analyzed.