Abstract: In this paper,considers the singular perturbation of boundary value problems for second order system of integro-differential equations. Under the suitable conditions the cxistence of the solution is proved and a asymptotic expansion of the solution and the estimation of the corresponding remainder term are geven by the asymptotic analysis method and the diagonalization technique. Then the results are applied to the singularly perturbed boundary value problem for the third order systems of ordinary differential equations. Finally a uniformly valid asymptotic expansion of the solution is obtained as well.

Key words: Integro-differential equation systems, Boundary value problems, Singular perturbation