  We describe a class of (2,2) superconformal field theories obtained by
fibering a Landau-Ginzburg orbifold CFT over a compact Kaehler base manifold.
While such models are naturally obtained as phases in a gauged linear sigma
model, our construction is independent of such an embedding. We discuss the
general properties of such theories and present a technique to study the
massless spectrum of the associated heterotic compactification. We test the
validity of our method by applying it to hybrid phases of linear models and
comparing spectra among the phases.
