It is shown that binary correspondences provide a simple and adequate formalization for the main components of problems (the condition of a problem, its data and unknowns), their basic properties and constructions (solvability and unique solvability of a problem, inverse problem, composition and restriction of problems), make it possible to formalize topological problems and related properties (stability, correctness), and also speak of parametrizations of problems and dependence of solutions on parameters.

As an example, a singularly perturbed system is considered of ordinary differential equations which describes a process of chemical kinetics and burning.