Abstract: In this paper, we consider a singularly perturbed problem of a kind of quasilinear hyperbolic-parabolic equations, subject to initial-boundary value conditions with moving boundary: When certain assumptions are satisfied and e is sufficiently small, the solution of this problem has a generalized asymptotic expansion (in the Van der Corput sense), which takes the sufficiently smooth solution of the reduced problem as the first term, and is uniformly valid in domain Q where the sufficiently smooth solution exists.The layer exists in the neighborhood of t = 0.This paper is the development of references [3-5].

Key words: singular perturbation, moving boundary, asymptotic expansion