If sneutrinos are the lightest supersymmetry partners and R-parity is not conserved, the process e + e − →νν can have striking signatures due to the decay modes ν → ℓ + ℓ ′− orν → qq ′ . 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 massm ν = 80 GeV and maybe beyond; four-jet signals should be detectable up tom ν = 70 GeV, but would probably be obscured thereafter by W W background.Searches for supersymmetry (SUSY) particles depend considerably on the identity of the lightest SUSY partner (LSP), usually believed to be a neutralino [1]. if approximately degenerate sneutrinosν α are the LSP and decay by RPV processes. We ignore single-SUSY-particle production [7,10], that can in principle take place with a lower threshold via RPV interactions, because the latter are either known [7,8] or suspected to have much much smaller couplings than the gauge couplings which control Eq.(1).Sneutrino pair production proceeds via t-channel exchange of charginos χ+ R → ν eν e only) and via s-channel Z exchange, that together give the helicity amplitudesHere θ is the CM polar scattering angle, m χ + i are the chargino masses (i = 1 is the lightest), while cos 2 γ R is the mixing probability of the wino component in the lightest chargino; β = 1 − 4m 2 ν /s is the sneutrino CM velocity, s and t are the usual invariant squares of energy and momentum transfer, θ W is the weak angle. The differential cross section is then defined by dσ/d cos θ = Σ|M| 2 β/(128πs); we note that it contains an overall factor sin 2 θ , favoring wide angles with good experimental acceptance, well away from the beam-pipe. as in many models). We note thatν eνe production is considerably enhanced aboveν µνµ andν τντ production, due to the chargino-exchange contribution (with constructive interference). Adding all three flavors, Fig.1 indicates about 500 (75) events per 100 pb −1 luminosity at √ s = 190 GeV, form ν = 50 (80) GeV, which should be enough to establish a clear signal in this mass range and possibly beyond, modulo detection efficiency and background questions discussed below.If a sneutrino is the LSP, it can only decay by RPV. With the particle content of the minimal SUSY-SM (MSSM), the most general gauge-and SUSY-invariant Lagrangian includes the following terms that can mediate sneutrino decays[6]where L i and E λ ijk ⇒ν i → ℓ