  The Chern-Simons topological term dynamical generation in the effective
action is obtained at arbitrary finite density. By using the proper time method
and perturbation theory it is shown that $\mu^2 = m^2$ is the crucial point for
Chern-Simons. So when $\mu^2 < m^2 \mu$--influence disappears and we get the
usual Chern-Simons term. On the other hand when $\mu^2 > m^2$ the Chern-Simons
term vanishes because of non-zero density of background fermions. In particular
for massless case parity anomaly is absent at any finite density. This result
holds in any odd dimension as in abelian so as in nonabelian cases.
