  We consider a wide class of linear boundary-value problems for systems of
$r$-th order ordinary differential equations whose solutions range over the
normed complex space $(C^{(n)})^m$ of $n\geq r$ times continuously
differentiable functions $y:[a,b]\to\mathbb{C}^{m}$. The boundary conditions
for these problems are of the most general form $By=q$, where $B$ is an
arbitrary continuous linear operator from $(C^{(n)})^{m}$ to $\mathbb{C}^{rm}$.
We prove that the solutions to the considered problems can be approximated in
$(C^{(n)})^m$ by solutions to some multipoint boundary-value problems. The
latter problems do not depend on the right-hand sides of the considered problem
and are built explicitly.
