In this thesis, two new methods for solution of nonlinear system of equations f(x) = 0 using two decomposition techniques are established, first is Adomian decomposition technique and second is Varsha decomposition technique. We expand f(x) to second order then apply both of these techniques one by one. The convergence order of both these algorithms is three and efficiency index is p 1/d =1.442. The main benefit of this scheme is that we get root of function even after one or two iterations, obviously has minimum computational complexity as compare to previous systems. Both methods almost give the same results and convergence orders. In practice, for large scale problems, many iterative methods can be derived by using two decomposition techniques with some modifications in Newton Raphson method. The order of convergence of new iteration formulas can be derived analytically and with the help of Maple. Some examples are given to illustrate the performance and precision of new algorithms. These algorithms can be assumed as generalization of old methods for solving nonlinear equations.