we successfully apply the DTM to find numerical solutions for
linear and nonlinear system of ordinary differential equations. It is observed
that DTM is an effective and reliable tool for the solution of system of ordinary
differential equations. The method gives rapidly converging series solutions.The accuracy of the obtained solution can be improved by taking more terms in
the solution. In many cases,the series solutions obtained with DTM can be
written in exact closed form. The present method reduces the computational
difficulties of the other traditional methods and all the calculations can be
made simple manipulations. Several examples were tested by applying the
DTM and the results have shown remarkable performance.