  We study the wave propagation modes in the relativistic streaming pair plasma
of the magnetospheres of pulsars and magnetars, focusing on the effect of
vacuum polarization. We show that the combined plasma and vacuum polarization
effects give rise to a vacuum resonance, where ``avoided mode crossing'' occurs
between the extraordinary mode and the (superluminous) ordinary mode. When a
photon propagates from the vacuum-polarization-dominated region at small radii
to the plasma-dominated region at large radii, its polarization state may
undergo significant change across the vacuum resonance. We map out the
parameter regimes (e.g., field strength, plasma density and Lorentz factor)
under which the vacuum resonance occurs and examine how wave propagation is
affected by the resonance. Some possible applications of our results are
discussed, including high-frequency radio emission from pulsars and possibly
magnetars, and optical/IR emission from neutron star surfaces and inner
magnetospheres.
