Abstract. Sustainable development of tourism in the mountains is justified in terms of functional properties of the recreational environment on the example of the biosphere ecological concept and ecosystem framework approach for sustainable development of tеrrіtorіal rеcreatіonal systems. According to the authors, the buffer capacity of recreation system is the dominant factor determining the prospects for the sustainable development of tеrrіtorіal rеcreatіonal systems. The combination of theoretical and methodological foundations of the doctrine of functionally integral geosystems with the concept of multi-vector nature of recreational environment formation, allowed pointing out and specifying those tеrrіtorіal rеcreatіonal systems, which operate within a certain space. Tеrrіtorіal rеcreatіonal systems, according to the authors is a dynamic set with the purpose of anthropogenic subjects and processes recreation within Geosystems whose activities continually trigger environmental changes, quantitative and qualitative Geosystem parameters, and is under the influence of man-made changes. The sustainable development of tеrrіtorіal rеcreatіonal systems provides an organization of recreational activities in which territorial Geosystem does not go beyond homeostasis and increasing of a recreational load is limited by buffer capacity of tеrrіtorіal rеcreatіonal systems. In this paper, the mathematical formalization of sustainable development of tеrrіtorіal rеcreatіonal systems is suggested. It can be used for the following definition of the subject of research: tеrrіtorіal rеcreatіonal system that operates in the environment, is the set of subjects that formed from a set of internal components interconnected with each other and with the environment by set of connections which vary in the process of sustainable development in time and space according to the set of functions.