Recently it was shown that, in the framework of superstring-inspired E
6 models, the presence of generation-dependent discrete symmetries all
ows us to construct a phenomenologically viable class of models in whi
ch the three generations of fermions do not have the same embedding wi
thin the fundamental 27-dimensional representation of E6. In this scen
ario these different embedding of the conventional fermions imply that
the left-handed charged leptons and the right-handed d-type quarks ar
e coupled in a nonuniversal way to the new neutral gauge bosons (Z(the
ta)) present in these models. It was also shown that a unique signatur
e for this scenario would be a deviation from unity for the ratio of c
ross sections for the production of two different lepton species in ee- annihilation. However, several different scenarios are possible, de
pending on the particular assignment chosen for e(L), mu(L), and tau(L
) and for the right-handed d-type quarks, as well as on the type of Z(
theta) boson. Such scenarios cannot be disentangled from one another b
y means of cross section measurements alone. In this paper we examine
the possibility of identifying the pattern of embeddings through measu
rements of polarized and unpolarized asymmetries for fermion pair prod
uction at the 500 GeV e+e- Next Linear Collider. We. show that it will
be possible to identify the different patterns of unconventional assi
gnments for the left-handed leptons and for the b(R) quark, for Z(thet
a) masses as large as approximately 1.5 TeV.