  We show how to formulate the phenomenon of gaugino condensation in a
super-Yang-Mills theory with a field-dependent gauge coupling described with a
linear multiplet. We prove the duality equivalence of this approach with the
more familiar formulation using a chiral superfield. In so doing, we resolve a
longstanding puzzle as to how a linear-multiplet formulation can be consistent
with the dynamical breaking of the Peccei-Quinn symmetry which is thought to
occur once the gauginos condense. In our approach, the composite gauge degrees
of freedom are described by a real vector superfield, $V$, rather than the
chiral superfield that is obtained in the traditional dual formulation. Our
dualization, when applied to the case of several condensing gauge groups,
provides strong evidence that this duality survives strong-coupling effects in
string theory.
