Abstract: In this paper we study the singularly penurbed boundary value problem: εy"=f(t,y,ε), y(0)=ξ(ε),y(1)=η(ε), where ε is a positive small parameter In the conditions:f_y(0,y,0)≥m,f_y(1,y,0)≥m₀ and f_y(t,y,ε)≥, we prove the existences, and uniformly valid asymptotic expansions of solutions for the given boundary value problems, and hence we improve the existing results.