  We compute the massless spectra of a set of flux vacua of the heterotic
string. The vacua we study include well-known non-Kahler T^2-fibrations over K3
with SU(3) structure and intrinsic torsion. Following gauged linear sigma
models of these vacua into phases governed by asymmetric Landau-Ginzburg
orbifolds allows us to compute the spectrum using generalizations of familiar
LG-orbifold techniques. We study several four- and six-dimensional examples
with N=2 spacetime supersymmetry in detail.
