The main aim of this paper is to demonstrate the feasibility and validity of the differential transform method, namely DTM. Therefore, the method has been applied to solve Hirota-Satsuma coupled KdV and coupled mKdV equations with initial conditions of two types. Hence, soliton solutions have been obtained easily as in . The DTM method is based on the Taylor series, but the series coefficients are calculated in an iterative manner by the help of T-transform. For many applications, series converges very quickly and closed form solutions can be reached. In the present work, illustrative examples have showed that the method provides a sequence of functions which converge to the exact solution of the aforementioned systems.