We study the interplay between T-duality, compactification and supersymmetry.
We prove that when the original configuration has unbroken space-time
supersymmetries, the dual configuration also does if a special condition is
met: the Killing spinors of the original configuration have to be independent
on the coordinate which corresponds to the isometry direction of the bosonic
fields used for duality. Examples of ``losers" (T-duals are not supersymmetric)
and ``winners" (T-duals are supersymmetric) are given.Comment: LaTeX file, 19 pages, U. of Groningen Report UG-8/94, Stanford U.
Report SU-ITP-94-19, QMW College Report QMW-PH-94-1