  Assuming that no supersymmetric signature will be found at the upgraded LEP
collider we derive lower bounds on the masses of the four neutralinos
$\tilde{\chi}_i^0$ in the Minimal Supersymmetric Standard Model (MSSM). We
consider the recently published results from the search for the light chargino
$\tilde{\chi}^\pm_1$ and the next-to-lightest neutralino $\tilde{\chi}^0_2$ at
LEP1.5 and study the consequences of possible future lower $\tilde{\chi}^\pm_1$
and $\tilde{\chi}^0_2$ mass limits between 65 and 95 GeV. For a chargino mass
bound of 66.8 GeV at LEP1.5, a massless neutralino is not excluded for
$\tan\beta < 1.2$. If either $\tan\beta > 2.3$ or the gluino mass
$m_{\tilde{g}} > 160$ GeV, we find $m_{\tilde{\chi}_1^0} > 28$ GeV. A possible
chargino bound $m_{\tilde{\chi}_1^\pm} > 95$ GeV at LEP2 would raise this bound
to 31 GeV (for all $\tan\beta$) or 44 GeV ($\tan\beta > 2$).
