  The zero-bias anomaly in the dependence of the tunneling density of states
$\nu (\epsilon)$ on the energy $\epsilon$ of the tunneling particle for two-
and one-dimensional multilayered structures is studied. We show that for a
ballistic two-dimensional (2D) system the first order interaction correction to
DOS due to the plasmon excitations studied by Khveshchenko and Reizer is partly
compensated by the contribution of electron-hole pairs which is twice as small
and has the opposite sign. For multilayered systems the total correction to the
density of states near the Fermi energy has the form $\delta \nu/\nu_0 = {max}
(| \epsilon |, \epsilon^*)/4\epsilon_F$, where $\epsilon^*$ is the plasmon
energy gap of the multilayered 2D system. In the case of one-dimensional
conductors we study multiwall nanotubes with the elastic mean free path
exceeding the radius of the nanotube. The dependence of the tunneling density
of states energy, temperature and on the number of shells is found.
