  We study a quantum particle in a tilted honeycomb lattice in the
tight-binding approximation. First we discuss the particle eigenstates, i.e.,
the stationary Wannier-Stark states. These states are proved to be extended
states for the rational directions of the static field and localized states for
the irrational directions. We find energy bands of the extended states and
analyze the localized states. It is shown, in particular, that the localized
`honeycomb' Wannier-Stark states are chaotic states with irregular dependence
of the localization length on the static field magnitude. Second we discuss
Bloch oscillations of the quantum particle. Irregular Bloch oscillations for
irrational directions are observed.
