  Neutralino and tau slepton pair production can naturally produce an excess of
tau lepton pairs at the current LEP collider energies. We describe the
constraints this has on the values of the mass parameters in the softly broken
Supersymmetric Lagrangian, and consider the consequences for superpartner
production at LEP and at the Fermilab Tevatron collider. The pair production of
the LSP and a heavier neutralino, followed by a 2-body decay to a tau slepton
and tau lepton, is consistent with the present LEP data, predicts a chargino
mass below 125 GeV, and provides an interesting Cold Dark Matter component,
with a relic matter density of .1-.2.
