In the framework of gauge-mediated supersymmetry breaking models pair production of the lightest neutralinos, scalar leptons, or charginos at LEPII gives rise to interesting signals involving multilepton final states and missing energy. In the parameter space where the scalar tau, $\tilde{\tau}_1$, is the next-to-lightest supersymmetric particle, we identify three interesting regions, which give rise to distinctly different final states: (i) 2 $\tau$-leptons plus missing energy, (ii) 4 charged leptons plus missing energy where in some regions all four are $\tau$-leptons, or (iii) six charged leptons, of which four are $\tau$-leptons and the other two are electrons or muons, plus missing energy. We study in detail the size of these regions in the parameter space of gauge-mediated models and give cross section contours in these regions for various LEPII energies. We also discuss the possibility of chargino-pair production at LEPII.
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