The article deals with the problem of creating a mathematical apparatus for implementing self-adaptive properties of applied software systems. Self-adaptability is the ability of software to modify its own srtucture and behavior under the influence of external factors (unforeseen at compile stage) by forming new system feedbacks on the basis of internal and external data flows. The key issue here is the mathematical description of possible options for structural and behavioural system changes. The proposed mathematical model is based on the author's concept of reflection according to which a software system is able to generate and embed in its structure new feedbacks due to mining own behavioral information. Software that use this self-adaptive mechanism named reflective systems.