The monograph attempts to create a unified theory of the dissipative structures of Turing-Prigozhin for systems of parabolic and hyperbolic equations with low diffusion. To this end, special asymptotic methods are developed to study the problems of the existence and stability of high-mode stationary modes in singularly perturbed systems. allowing to obtain very subtle statements about the unlimited growth of the number of stable dissipative structures (as stationary , as well as -periodic in time) with a decrease in diffusion coefficients and with fixed other parameters. General ideas about the nature of autowave processes in nonlinear environments with low diffusion are developed on the basis of a systematic analysis of the buffering phenomenon, high-water attractors and diffusion chaos .. Applications from radiophysics, mechanics, ecology, nonlinear optics and combustion theory are considered. For senior students, graduate students of mathematical and physical faculties of universities, specialists in applied mathematics, oscillation theory, nonlinear dynamics .