  A pronounced asymmetry of magnetoresistance with respect to the magnetic
field direction is observed for NbSe$_3$ crystals placed in a magnetic field
perpendicular to their conducting planes. It is shown that the effect persists
in a wide temperature range and manifests itself starting from a certain
magnetic induction value $B_0$, which at $T=4.2$ K corresponds to the
transition to the quantum limit, i.to the state where the Landay level
splitting exceeds the temperature.
