Analysing many phenomena , shows deviation from statistical mechanics of Boltzmann-Gi. It is not possible to phenomena that have probability distribution in the power iow form, by using Boltzmann-Gi statistical mechanics which has a probability distribution in exponential form. Most of thes problems have long-range intraction, long-term memories or fractal properties. The day-by-day development of these problems insists on defining a more general definition for statistical mechanics. In 1988, Tsallis introduced another kind of entropy that is related to a parameter, . Tsallis entropy and its related statistical mechanics are called nonextensive. This dissertation another generalization of Tsallis entropy according to a two parameter entropy and Sharma-Mittal's entropy are introduced and also the properties of this entropy such as composability, concavity, ets will be considered.