Indirect limits on the mass of the Lightest neutralino are derived fro
m the results of searches for charginos, neutralinos, and sleptons per
formed with data taken by the ALEPH Collaboration at centre-of-mass en
ergies near the Z peak and at 130 and 136 GeV. Within the context of t
he Minimal Supersymmetric Standard Model and when M(<(nu)over tilde>)
greater than or equal to 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 includi
ng Higgs mass constraints and requiring that radiative electroweak sym
metry breaking occur, more stringent bounds on M(chi) as a function of
tan beta are derived.