We shall consider the boundary layer problems described by second order differential equation with small perturbation parameter multiplying the highest derivative and the appropriate boundary conditions of nonlocal type. This kind of problems represent mathematical models of a large number of phenomena in catalytic processes in chemistry and biology, as well as in the theory of semiconductors in electronics. The solution inside the boundary layer will be constructed using truncated orthogonal series, and the solution out of the layer will be approximated by the solution of the reduced problem. The layer will be determined in terms of the perturbation parameter and the degree of the chosen truncated orthogonal series.