V. B. Bagdonavi\v{c}ius, M. S. Nikulin On parametric inference for step-stress models Email: nikou@mi2s.u-bordeaux2.fr Applications of the additive accumulation of damages (AAD) and the proportional hazards (PH) models in accelerated life testing with step-stresses are discussed. A new model including both of them is proposed. It is more natural then PH model and wider then the AAD model. Maximum likelihood function construction is discussed.