In this paper, the combined Laplace transform-Adomian decomposition method is presented to solve systems of n" order differential equations. Theoretical considerations are being discussed. The Laplace transform and Adomian decomposition methods are combined and an n" iterative formula is generated. Some examples are presented to show the ability of the method for linear and non-linear systems of differential equations. The results obtained are in good agreement v, i th the exact solution as indicated by a small percentage error.