We show how to formulate the phenomenon of gaugino condensation in a s
uper-Yang-Mills theory with a field-dependent gauge coupling described
with a linear multiplet. We prove the duality equivalence of this app
roach with the more familiar formulation using a chiral superfield. In
so doing, we resolve a longstanding puzzle as to how a linear-multipl
et formulation can be consistent with the dynamical breaking of the Pe
ccei-Quinn symmetry which is thought to occur once the gauginos conden
se. In our approach, the composite gauge degrees of freedom are descri
bed 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.