Lifetime of a structure is considered as the time needed to initiate some macroscopic crack, propagation of which is then calculated with the help of Fracture Mechanics concepts. The paper gives a brief discussion of the possibilities of lifetime parametric relations, based on strain variables, in the high-temperature range. Alternative approaches based on Continuous Damage Mechanics are then developed and discussed; they introduce internal damage variables, describing the progressive deterioration of the material before macroscopic crack initiation. A particular definition of damage, based on the effective stress concept, gives a macroscopic measure, which constitutes a guideline to the development of differential damage equations. Some examples show the possibilities of these approaches and deal with nonlinear cumulative effects (or sequence effects) and creep-fatigue interaction.