Abstract: A class of Robin boundary value problems are considered. Under suitable conditions, firstly, the formal outer solution of the original problem is constructed with the expansion method of power series. Secondly, shock layer corrective term near the interior point in the interval is constructed via the transformation of stretched variable. Finally, the existence and uniform validity in the whole interval and asymptotic behavior of solution for the original Robin boundary value problems are proved by means of the theory of differentialinequalities. The satisfying results are obtained.

Key words: singular perturbation, quasilinear, boundary value problem, shock solution