  The $e^- e^-$ mode with lepton number $L=+2$ of the initial state is
particularly suitable for studying lepton and flavor number violating reactions
(LFV). In this brief report we give a summary of the study of two loop-level
reactions which violate lepton and flavor numbers: we first consider seesaw
type models with heavy Majorana neutrinos at the TeV scale and study the
reactions $e^{-}e^{-} \to \ell^{-}\ell^{-}$, and then similar reactions
$e^{-}e^{-} \to \ell^{-}e^{-}$ ($\ell=\mu,\tau$) in supersymmetric models where
LFV is due to slepton mixing.
