  Indirect limits on the mass of the lightest neutralino are derived from the
results of searches for charginos, neutralinos, and sleptons performed with
data taken by the ALEPH Collaboration at centre-of-mass energies near the Z
peak and at 130 and 136 GeV. Within the context of the Minimal Supersymmetric
Standard Model and when $M_{\tilde\nu}\ge 200$ GeV/c^2, the bound $M_\chi>12.8$
GeV/c^2 at the 95\% confidence level applies for any $\tan\beta$. The impact of
lighter sneutrinos is presented in the framework of SUSY grand unified
theories; a massless neutralino is allowed only for a narrow range of
$\tan\beta$, $\mu$, and the scalar mass parameter $m_0$. Finally, by including
Higgs mass constraints and requiring that radiative electroweak symmetry
breaking occur, more stringent bounds on $M_\chi$ as a function of $\tan\beta$
are derived.
