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 Mν˜⩾200GeV/c2 , the boundM x > 12.8 GeV/c 2 at the 95% confidence level applies for any tanβ. 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 tanβ,μ, and the scalar mass parameterm 0. Finally, by including Higgs mass constraints and requiring that radiative electroweak symmetry breaking occur, more stringent bounds onM x as a function of tanβ are derived.