  In this work we prove the local multiplicity at most one theorem underlying
the definition and theory of local $\gamma$-, $\epsilon$- and $L$-factors,
defined by virtue of the generalized doubling method, over any local field of
characteristic 0. We also present two applications: one to the existence of
local factors for genuine representations of covering groups, the other to the
global unfolding argument of the doubling integral.
