  We investigate the presence of discrete gauge symmetries in Grand Unification
models based in $SO(10)$ and $E_6$. These models include {\it flipped} and {\it
unflipped} $SU(5)$, $SU(4)\!\times\! SU(2)_L\!\times\! SU(2)_R$,
$SU(3)_C\!\times\! SU(3)_L\!\times\! SU(3)_R$, and $SU(6)\!\times\! SU(2)$.
Using the Dynkin formalism we find the $U(1)$ subalgebras contained in the
unified groups, give an expression for the Higgs fields that preserve each
discrete symmetry, and determine the low-energy matter content implied by
chirality. We discuss two $Z_2$ and three $Z_3$ nonequivalent cases. Among the
possibilities found, only the usual $Z_2$ matter parity (R-parity) of
supersymmetric extensions is consistent with a minimal matter content with no
right- handed neutrinos, extra Higgs doublets, or nonstandard {\it down}-type
quarks.
