  The premetric approach to electrodynamics provides a unified description of a
wide class of electromagnetic phenomena. In particular, it involves axion,
dilaton and skewon modifications of the classical electrodynamics. This
formalism emerges also when the non-minimal coupling between the
electromagnetic tensor and the torsion of Einstein-Cartan gravity is
considered. Moreover, the premetric formalism can serve as a general covariant
background of the electromagnetic properties of anisotropic media. In the
current paper, we study wave propagation in the premetric electrodynamics. We
derive a system of characteristic equations corresponded to premetric
generalization of the Maxwell equation. This singular system is characterized
by the adjoint matrix which turns to be of a very special form -- proportional
to a scalar quartic factor. We prove that a necessary condition for existence a
non-trivial solution of the characteristic system is expressed by a unique
scalar dispersion relation. In the tangential (momentum) space, it determines a
fourth order light hypersurface which replaces the ordinary light cone of the
standard Maxwell theory. We derive an explicit form of the covariant dispersion
relation and establish it'salgebraic and physical origin.
