  We describe a semi-analytic approach to the two-band Ginzburg-Landau theory,
which predicts the behavior of vortices in two-band superconductors. We show
that the character of the short-range vortex-vortex interaction is determined
by the sign of the normal domain - superconductor interface energy, in analogy
with the conventional differentiation between type-I and type-II
superconductors. However, we also show that the long-range interaction is
determined by a modified Ginzburg-Landau parameter $\kappa^*$, different from
the standard $\kappa$ of a bulk superconductor. This opens the possibility for
non-monotonic vortex-vortex interaction, which is temperature-dependent, and
can be further tuned by alterations of the material on the microscopic scale.
