Abstract: The advances in the antidissipativc method for solving gas dynamic equations arc reviewed. The antidissipativc mixed difference scheme proposed by the author of this paper may be used to obtain not only Beam-Warming scheme and Jameson scheme with free parameters, but also "TVD" Scheme. In the second part of this paper we discuss antidissipative mixed difference scheme with parameters. The third part deals with antidissipative mixed scheme containing no parameters. The applications of antidissipative mixed d...