An attempt has been made to systematize the criterion for the crack initiation, the crack growth and the final fracture in creep, fatigue and creep-fatigue interaction conditions at high temperatures. Reference has been made to the systematically designed studies performed hitherto by the authors and colleagues, including the comparative study on the similarity and the dissimilarity between creep and fatigue. Further research as complexity science and engineering is emphasized. © 2002 Elsevier Science Ltd. All rights reserved.