Abstract: In this paper, an algorithm is developed for using the G’ /G-expansion method to obtain exact solutions for discrete nonlinear systems. Applying this method, some kinds of travelling wave solutions for AL system and Toda lattice system are derived. These solutions are expressed by hyperbolic function, trigonometric function and rational function with parameters. When the parameters are taken as special values, some known solutions including kink-type solitary wave solution and singular travelling wave solution are recovered. It is shown that the developed algorithm is effective and direct. It also can be used for many other nonlinear differential-difference equations in mathematical physics. 

Key words: an algorithm, AL system, Toda lattice system, exact solutions