Abstract: Moduli of smoothness are tools for peoples working in approximation theory real analysis, numerical analysis, differential equations, functional analysis and statistical estimation. Differentiating the functions many times to know the number of its derivative is a too groud method. In approximation theory, A sutable tool for measuring smoothness of function is the modulus of smoothness. In Ditizian and Totik the failure of the elassical moduli of smoothness to solve some problems in characterizing the behavior of the degree of best approximation, make Ditizian and Totik introduced a tool for measuring smoothness. Called Ditizian and Totik modulus of smoothness in our paper we introduce some versions of moduli of smoothness and then we show that they are equivalent to Ditizian-Totik (DT) modulus of smoothness of function in L_p[-1,1] spaces for 0<p<1.