  We consider the E8 x E8 heterotic string theory compactified on Calabi-Yau
manifolds with bundles containing abelian factors in their structure group.
Generic low energy consequences such as the generalised Green-Schwarz mechanism
for the multiple anomalous abelian gauge groups are studied. We also compute
the holomorphic gauge couplings and induced Fayet-Iliopoulos terms up to
one-loop order, where the latter are interpreted as stringy one-loop
corrections to the Donaldson-Uhlenbeck-Yau condition. Such models generically
have frozen combinations of Kaehler and dilaton moduli. We study concrete
bundles with structure group SU(N) x U(1)^M yielding quasi-realistic gauge
groups with chiral matter given by certain bundle cohomology classes. We also
provide a number of explicit tadpole free examples of bundles defined by exact
sequences of sums of line bundles over complete intersection Calabi-Yau spaces.
This includes one example with precisely the Standard Model gauge symmetry.
