  Gauging $B-L$ symmetry provides a simple realization of the seesaw mechanism
in a naturally anomaly free extension to the MSSM gauge group, $SU(3)_c\times
SU(2)_L\times U(1)_Y \times U(1)_{B-L}$. However, as we discuss in here, it
turns out that the simplest $B-L$ extension of the MSSM may change some of the
conceptions about the path for gauge unification as well as to affect the
predicted spectrum of the supersymmetric particles at low energy. For instance,
the coupling $g_{B-L}$ ended up to be smallest of all of them and the lightest
gaugino is the one related to $B-L$. RGE also help to understand the
spontaneous breaking of the $U(1)_{B-L}$ and the vacuum expectation value of
the sneutrino at low energies, which occurs in this type of models.
