  We analyze the Wannier-Stark spectrum of a quantum particle in tilted
two-dimensional lattices with the Bloch spectrum consisting of two subbands,
which could be either separated by a finite gap or connected at the Dirac
points. For rational orientations of the static field given by an arbitrary
superposition of the translation vectors the spectrum is a ladder of energy
bands. We obtain asymptotic expressions for the energy bands in the limit of
large and weak static fields and study them numerically for intermediate field
strength. We show that the structure of energy bands determines the rate of
spreading of a localized wave packets which is the quantity measured in
laboratory experiments. It is shown that wave-packet dispersion becomes a
fractal function of the field orientation in the long-time regime of ballistic
spreading.
