  Given a linear ordinary differential equation (ODE) on $\RE$ and a set of
interface conditions at a finite set of points $I \subset \RE$, we consider the
problem of determining another differential equation whose {\it global}
solutions satisfy the original ODE on $\RE \backslash I $, and the interface
conditions at $I $. Using an extension of the product of distributions with
non-intersecting singular supports presented in [L. H\"ormander, The Analysis
of Linear Partial Diffe\-rential Operators I, Springer-Verlag, 1983], we
determine an {\it intrinsic} solution of this problem, i.e. a new ODE,
satisfying the required conditions, and strictly defined within the space of
Schwartz distributions. Using the same formalism, we determine a singular
perturbation formulation for the $n$-th order derivative operator with
interface conditions.
