  Quantum symmetries of four-dimensional superstrings are frequently realized
in an anomaly-cancellation mode in the effective low-energy supergravity. The
massless antisymmetric tensor plays an important r\^ole in this mechanism and
the choice of its supersymmetric description, using either a chiral or a linear
multiplet, appears to introduce significant conceptual and practical
differences at the string loop level. This paper reviews the construction of
loop-corrected string effective supergravities with the dilaton and
antisymmetric tensor embedded in a linear multiplet. Using anomaly cancellation
and the linear multiplet allows to obtain an all-order renormalization-group
invariant effective lagrangian for a pure gauge sector with field-dependent
gauge coupling constant.
  Presented at the Workshop "Physics from Planck Scale to Electroweak Scale",
  Warsaw, Poland, September 1994.
