Аннотация:The aim of this work is to explain the role played by the Fock quantization of canonical transformations in the construction of the global semiclassical (high-frequency) asymptotic approximation. This role may well pass unnoticed as long as one deals with nondegenerate differential equations. However, the situation is different for some classes of equations with degeneration, where the Fock quantization of canonical transformations becomes instrumental in the construction of asymptotic solutions.