The work is devoted to completing of the asymptotic theory construction of the transient wave propagation in thin-walled shells of revolution under tangential type impact edge longitudinal loads. The previously developed asymptotically approximate equations of such components as the membrane component according to the Kirchhoff-Love shell theory, the parabolic boundary layer in the vicinity of the membranewave front, the high-frequency short-wave component, and the hyperbolic boundary layer in the vicinity of the dilatational wave front are used. The completeness of the description of nonstationary waves using these components is proved. For this purpose, the overlap regions of neighboring components in the phase plane (place) are identified: asymptotic estimates of the region boundaries are found and the coincidence of the equation asymptotic in these areas is proved. The construction of the asymptotic theory under consideration is not limited to the development of a scheme for dividing a nonstationary stress-strain state into components with the different variability and dynamicity indices and the derivation of equations for these components. Algorithms for analytical solutions of boundary value problems have been developed for all components, based on various types of power series expansions for a small parameter of shell thickness. Different integral transformations, methods of front asymptotics, methods of decomposition by special functions and other are used. The effectiveness of the developed methods is illustrated by the example of problems for a spherical shell.