Abstract: Using the methods of boundary function and fractional steps, the author constructed the asymptotic solution of steptype  contrast structure for a class of weak nonlinear singularly perturbed differentialdifference equation, and obtained the time t=t* to produce a contrast structure. By means of sewing method, the author proved the existence of the smooth solution of interior layer and the uniform validity of the asymptotic solution of the form.

Key words: asymptotic expansion, boundary function, contrast structure, differentialdifference equation