  We discuss the pair production of gluinos in electron-positron annihilation
at LEP, in a model with soft supersymmetry breaking, allowing for mixing
between the squarks. In much of the parameter space of the Minimal
Supersymmetric Model (MSSM) the cross section corresponds to a $Z$ branching
ratio above $10^{-5}$, even up to $10^{-4}$. A non-observation of gluinos at
this level restricts the allowed MSSM parameter space. In particular, it leads
to lower bounds on the soft mass parameters in the squark sector.
