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.