Gaugino Masses in Modular Invariant Supergravity

We calculate gaugino masses in string-derived models with hidden-sector gaugino condensation. The linear multiplet formulation for the dilaton superfield is used to implement perturbative modular invariance. The contribution arising from quantum effects in the observable sector includes the term recently found in generic supergravity models. A much larger contribution is present if matter fields with Standard Model gauge couplings also couple to the Green-Schwarz counter term. We comment on the relation of our K"ahler U(1) superspace formalism to other calculations.