  We investigate the cosmological constraints on exotic stable matter states
which arise in realistic free fermionic superstring models. These states appear
in the superstring models due to a ``Wilson--line'' breaking of the unifying
non--Abelian gauge symmetry. In the models that we consider the unifying
$SO(10)$ gauge symmetry is broken at the string level to $SO(6)\times SO(4)$,
$SU(5)\times U(1)$ or $SU(3)\times SU(2)\times U(1)^2$. The exotic matter
states are classified according to the patterns of the $SO(10)$ symmetry
breaking. In $SO(6)\times SO(4)$ and $SU(5)\times U(1)$ type models one obtains
fractionally charged states with $Q_{\rm e.m.}=\pm1/2$. In $SU(3)\times
SU(2)\times U(1)^2$ type models one also obtains states with the regular
charges under the Standard Model gauge group but with ``fractional'' charges
under the $U(1)_{Z^\prime}$ symmetry. These states include down--like color
triplets and electroweak doublets, as well as states which are Standard Model
singlets. By analyzing the renormalizable and nonrenormalizable terms of the
superpotential in a specific superstring model, we show that these exotic
states can be stable. We investigate the cosmological constraints on the masses
and relic density of the exotic states. We propose that, while the abundance
and the masses of the fractionally charged states are highly constrained, the
Standard Model -- like states, and in particular the Standard Model singlet,
are good dark matter candidates.
