Scientific researches are devoted to the development of the theory of functional stability of ecosystems, as the stability of the functional of ecological safety. The conceptual (system of views of ensuring the ecosystem functional stability) and theoretical (the idea is comprehensively researched using scientifically-based approaches, methods, techniques, algorithms and mathematical models) of the theory of functional stability of ecosystems are offered. The theoretical bases of sustainable development of technogenically loaded ecosystems under conditions of synergism of components of ecological danger of different genesis are considered. On the example of the model of interaction of pollution of aquatic ecosystem its stability is investigated. The processes are described by Lot-Volterra type equations. This uses a modification of the first Lyapunov method, which is designed to study the stability of aquatic ecosystems of non-autonomous differential equations. For this purpose, a family of linear operators is constructed and the stability of systems of differential equations is determined by the signs of their logarithmic norms. Criteria for stability and asymptotic stability of fixed points by Lyapunov were obtained in the model of interaction of pollution with the aquatic ecosystem. The proposed method can be used to study a wide range of other ecosystems.