  We introduce the most general class of linear boundary-value problems for
systems of first-order ordinary differential equations whose solutions belong
to the complex H\"older space $C^{n+1,\alpha}$, with $0\leq n\in\mathbb{Z}$ and
$0\leq\alpha\leq1$. The boundary conditions can contain derivatives $y^{(r)}$,
with $1\leq r\leq n+1$, of the solution $y$ to the system. For
parameter-dependent problems from this class, we obtain constructive criterion
under which their solutions are continuous in the normed space $C^{n+1,\alpha}$
with respect to the parameter.
