  In the last few years physicists have been looking at $SO(10)$ GUT models
with renewed attention because it has been realized that the SU(5) minimal
model cannot unify the strong, electromagnetic and weak interactions in a way
consistent with the experimental values of $\alpha(M_Z)$, $\si$ and
$\alpha_S(M_Z)$. In this paper we derive lower limits on neutrino masses,
relevant for cosmology and for the solar-neutrino problem, from necessary
consistency conditions on a class of $SO(10)$ models with $\sq$ or $\stt$
intermediate gauge symmetry.
