  We study the propagation of an oscillatory electromagnetic field inside a
Weyl semimetal. In conventional conductors, the motion of the charge carriers
in the skin layer near the surface can be diffusive, ballistic, or
hydrodynamic. We show that the presence of chiral anomalies, intrinsic to the
massless Weyl particles, leads to a hitherto neglected nonlocal regime that can
separate the normal and viscous skin effects. We propose to use this novel
regime as a diagnostic of the presence of chiral anomalies in optical
conductivity measurements. These results are obtained from a generalized
kinetic theory which includes various relaxation mechanisms, allowing us to
investigate different transport regimes of Weyl semimetals.
