  In theories with unstable particles, unitarity is satisfied by the inclusion
of only stable states in unitarity sums. Hence unitarity cuts are not to be
taken through unstable particles. This raises a challenge to the generalized
unitarity method, whose aim is to reconstruct amplitudes by analyzing sets of
unitarity cuts. Nevertheless, under some general physical conditions, and
perhaps some methodological modifications, we prove that the method is still
reliable for one-loop amplitudes containing resonances. We discuss some simple
examples which illustrate these features.
