While a complete description of the moduli space of heterotic compactification string vacua it is yet unknown, a subset of it can be realized as a GLSM (gauged linear sigma-model). The GLSM structure allows us to probe the whole moduli space by simply varying the Fayet-Ilioupolous parameters searching for points/limits where computations can be done. Among these we have, for example, Landau-Ginzburg limits where the target space is just a point, obtained by shrinking down the compactfication space, and massless excitations interact via a superpotential. A more common phase is a hybrid, where the compactification space is a certain base space B with non-negative curvature; here, in addition to the modes associated to the motion along the base, which is assumed to be large, there are massless modes transverse to it, i.e. along the fiber, all of these interacting via an effective superpotential. In this talk I present a technique we developed for computing the complete massless spectrum in hybrid models with Landau-Ginzburg fibers.