If sneutrinos are the lightest supersymmetry partners and $R$-parity is not conserved, the process $e^+e^- to tilde {bar u} tilde { u}$ can have striking signatures due to the decay modes $tilde{ u}toell^+ell^-$ or $tilde{ u}to q bar q$. 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 $tilde {m}_ u = 80$ GeV and maybe beyond; four-jet signals should be detectable up to $tilde {m}_ u = 70$ GeV, but would probably be obscured thereafter by $WW$ background.
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