  If sneutrinos are the lightest supersymmetry partners and $R$-parity is not
conserved, the process $e^+e^- \to \tilde {\bar\nu} \tilde {\nu}$ can have
striking signatures due to the decay modes $\tilde{\nu}\to\ell^+\ell'^-$ or
$\tilde{\nu}\to q \bar q'$. We present cross section formulas and discuss event
rates and detection at the upgraded $e^+e^-$ collider LEP. Four-lepton signals
should be detectable up to sneutrino mass $\tilde {m}_\nu = 80$ GeV and maybe
beyond; four-jet signals should be detectable up to $\tilde {m}_\nu = 70$ GeV,
but would probably be obscured thereafter by $WW$ background.
