  We investigate a generalized two-dimensional Weyl Hamiltonian, which may
describe the low-energy properties of mechanically deformed graphene and of the
organic compound alpha-(BEDT-TTF)_2I_3 under pressure. The associated
dispersion has generically the form of tilted anisotropic Dirac cones. The tilt
arises due to next-nearest-neighbor hopping when the Dirac points, where the
valence band touches the conduction band, do not coincide with crystallographic
high-symmetry points within the first Brillouin zone. Within a semiclassical
treatment, we describe the formation of Landau levels in a strong magnetic
field, the relativistic form of which is reminiscent to that of graphene, with
a renormalized Fermi velocity due to the tilt of the Dirac cones. These
relativistic Landau levels, experimentally accessible via spectroscopy or even
a quantum Hall effect measurement, may be used as a direct experimental
verification of Dirac cones in alpha-(BEDT-TTF)_2I_3.
