  We show how the level matching condition in six dimensional, abelian and
supersymmetric orbifolds of the E_8 x E_8 heterotic string can be given
equivalently in terms of fractional gauge and gravitational instanton numbers.
This relation is used to restate the classification of the orbifolds in terms
of flat bundles away from the orbifold singularities under the constraint of
the level matching condition. In an outlook these results are applied to
Kaluza-Klein monopoles of the heterotic string on S^1 in Wilson line
backgrounds.
