<正> In this paper,using the method of differential inequalities,we study the existence ofsolutions and their asymptotic behavior,as ε→0+,of Dirichlt problem for second orderquasilinear systems.Depending on whether the reduced solution u(t)has or does not havea continuous first-derivative in(a,b),we study two types of asymptotic behaviour,thusleading to the phenomena of boundary and angular layers.