  We derive the precise relation between level matching condition and
fractional instanton numbers in six dimensional, abelian and supersymmetric
orbifolds of E8 x E8 heterotic string theory. The fractional part of the two E8
instanton numbers is explicitly calculated in terms of the gauge twist. This
relation is then used to show that the classification of these orbifolds can be
given in terms of flat bundles away from the orbifold singularities under the
only constraint that the sum of the fractional parts of the gauge instanton
numbers match the fractional part of the gravitational instanton number locally
at every fixed point. This directly carries over to M-theory on S^1/Z_2
