Of late the demands of industry in creating new composite and functional materials with present properties stimulated an increased interest to the investigation of processes which occur in the detonation technologies of complex chemical composition with an additive of disperse particles. The collection includes a series of papers presented at the 3d International Conference "Lavrentyev Readings on Mathematics, Mechanics, and Physics" (Novosibirsk, 1990),was held by the Hydrodynamics Institute under the support of the Presidium of the Siberian Branch of the USSR Academy of Sciences to stimulate the international cooperation of the leading international centers. In the framework of this Conference the Round Table seminar was held by Prof. A. Borissov and Prof. V. Mi trofanov devoted to "Dynamic Structure of Detonation in Gaseous and Dispersed Media". The idea to hold such Round Table was supported by Chairman of Organizing Committee academician Prof. V.Titov from Hydrodynamics Institute, and academician Prof. V. Nakoryakov and also his Institute of Thermophysics. The main ideas discussed at the Round Table were presented in the form of papers which reflected present situation of the problem of dynamic structure of the detonation waves in gaseous and dispersed media. The basic experimental facts concerning of complicated mul ti­ dimensional non-stationary structure both of the detonation wave and its front surface, generation of the cell structure, the effect of transverse waves, obstacles, channel geometry etc. on the transition from dynamic regime to stationary structure are represented in the fist three papers.