Two new classes of analytic functions with positive coefficients. M(k,a) and N(k,a) are introduced. Using some methods in complex analysis, the inclusion relations are obtained by the formulas *. By some calculations and using series properties, sufficient conditions of coefficients inequality are obtained. Using lemma 1 necessary conditions of coefficients inequality are obtained. Further, growth theorems, convex linear relations for the class are investigated by coefficients inequality. The results are accurate.(* Indicates a formula, please see the full text)