  We derive the general upper bounds on the mass of the lightest neutralino, as
a function of the gluino mass, in different supersymmetry breaking models with
minimal particle content and the standard model gauge group. This includes
models with gravity mediated supersymmetry breaking (SUGRA), as well as models
with anomaly mediated supersymmetry breaking (AMSB). We include the
next-to-leading order corrections in our evaluation of these bounds. We then
expand the mass matrix in powers of M_Z/mu, and find the upper bound on the
mass of the lightest neutralino from this expansion. By scanning over all of
the parameter space, we find that the bound we have obtained can be saturated.
We compare the general upper bound on the lightest neutralino mass to the upper
bound that is obtained when the radiative electroweak symmetry breaking
scenario is assumed.
