The promising ways to predict the durability of polymer composites under the influence of extreme factors of the external environment and operational loads are investigated. The possibilities of effective predicting the defining characteristics (the residual life, strength, reliability, and durability) of composites are studied based on the information received in the first years of their operation. The development of generalized durability models of composites under extreme conditions is based on the main provisions of the modern molecular kinetic theory (MKT). This is due to the fact that chemical transformations in composites can occur both at intermolecular and intramolecular levels. On the basis of the modern MKT, the issue of matching the defining parameters of mathematical models calculated by solving prediction problems within the framework of formulated refined variational statements taking into account the results of experimental measurements at the macrolevel with the corresponding defining parameters of physical models describing molecular interactions at the microlevel is investigated. Results of computational experiments are presented.