Destruction of material is consided as process of accumulation of internal microdamages temporally. Conception of memory of material on carried it damages was introduced. formulation of direct and contrary problems of forecasting durability and longevity of polymers and compositions on basis of it in variables temperature – power conditions of test or exploitation was given. For solution of this promlems for materials with random type of memory consolidated principle of superposition damages was formulated. On basis of it solution of direct problem of forecasting was given. explanation of observed experimentally anomalies was given on diagrams temperature – power dependence of durability.