  An interesting prediction of a string-inspired {\em one-parameter}
$SU(5)\times U(1)$ supergravity model, is the fact that the lightest member
($\tilde t_1$) of the top-squark doublet $(\tilde t_1,\tilde t_2)$, may be
substantially lighter than the top quark. This sparticle ($\tilde t_1$) may be
readily pair-produced at the Tevatron and, if $m_{\tilde t_1}\lsim130\GeV$,
even be observed at the end of Run IB. Top-squark production may also be an
important source of sought-for top-quark signatures in the dilepton and
$\ell$+jets channels. Therefore, a re-analysis of the top data sample in the
presence of a possibly light top-squark appears necessary before definitive
statements concerning the discovery of the top quark can be made. Such a light
top-squark is linked with a light supersymmetric spectrum, which can certainly
be searched for at the Tevatron through trilepton and squark-gluino searches,
and at LEPII through direct $\tilde t_1$ pair-production (for $m_{\tilde
t_1}\lsim100\GeV$) and via chargino and Higgs-boson searches.
