The normal spline method is developed for the initial and boundary-value problems for linear integro-differential equations, probably being unresolved with respect to the derivatives, in Sobolev spaces of the arbitrary smoothness. It allows to solve a high-order systems without the reduction to first-order ones. The solving system can be arbitrary degenerate (with high differentiation index or irreducible to normal form). The method of nonuniform collocation grid creation for stiff problems is offered. Results of numerical solution to test problems are demonstrated. Supported by Russian Foundation for Basic Research, project N o 01-01-00731