  We show that one of the ways of obtaining consistency between the idea of
supersymmetric grand unification and an apparent low value of
$\alpha_{strong}(M_Z)\simeq .11$ indicated by several low energy experiments is
to have an intermediate scale corresponding to a local $B-L$ symmetry breaking
around the mass scale of $10^{10}$ to $10^{12}$ GeV. We discuss the realization
of this idea within the framework of supersymmetric $SO(10)$ grand unified
theories with spectra of particles derivable from simple superstring-inspired
versions of this model. We then study the $b-\tau$ mass unification within this
class of models and show that due to the influence of new gauge and Yukawa
interactions beyond the intermediate scale, the prediction of the $b$-quark
mass comes out well within the presently accepted values. We also discuss an
un-orthodox class of SUSY models inspired by some theoretical considerations
having two pairs of Higgs doublets at low energy and show that they also can
lead to unification with intermediate scales and low $\alpha_{s}(M_Z)$ as
desired.
