We consider an approximate scheme for treating a class of two-dimensional, singularly perturbed, exterior boundary value problems. Our scheme is a combination of boundary element and finite element methods. By introducing a factitious boundary, we divide the region into two regions, an inner and outer region. In the inner region, we employ the finite element method for solving the field equations under consideration with proper natural boundary conditions. These natural boundary conditions are obtained by solving the corresponding boundary integral equations. In the outer regions, solutions are expressed in terms of simple-layer potentials which are matched to the finite element solution on the factitious boundary. Error estimates and numerical experiments are included.