Summary: We consider a broad class of linear boundary-value problems for systems of \(m\) ordinary differential equations of order \(r\) known as general boundary-value problems. Their solutions \(y : [a, b] \rightarrow \mathbb{C}^m\) belong to the Sobolev space \((W_1^r)^m\) and the boundary conditions are given in the form \(By = q\), where \(B: (C^{( r - 1)})m \rightarrow \mathbb{C}^{ rm }\) is an arbitrary continuous linear operator. For this problem, we prove that its solution can be approximated in \((W_1^r)^m\) with arbitrary accuracy by the solutions of multipoint boundaryvalue problems with the same right-hand sides. These multipoint problems are constructed explicitly and do not depend on the right-hand sides of the general boundary-value problem. For these problems, we obtain estimates for the errors of solutions in the normed spaces \((W_1^r)^m\) and \((C^{( r - 1)})^m\).