  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.
