  We study the traversal times of electromagnetic pulses across dispersive
media with negative dielectric permittivity ($\varepsilon$) and magnetic
permeability ($\mu$) parameters. First we investigate the transport of optical
pulses through an electrical plasma and a negative refractive index medium
(NRM) of infinite and semi-infinite extents where no resonant effects come into
play. The total delay time of the pulse constitutes of the group delay time and
the reshaping delay time as analyzed by Peatross et al \cite{peatross}. For
evanescent waves, even with broadband width, the total delay time is negative
for an infinite medium whereas it is positive for the semi-infinite case.
Evidence of the Hartman effect is seen for small propagation distance compared
to the free space pulse length. The reshaping delay mostly dominates the total
delay time in NRM whereas it vanishes when $\varepsilon(\omega)=\mu(\omega)$.
  Next we present results on the propagation times through a dispersive slab.
While both large bandwidth and large dissipation have similar effects in
smoothening out the resonant features that appear due to Fabry-P\'{e}rot
resonances, large dissipation can result in very small or even negative
traversal times near the resonant frequencies. We investigate the traversal and
the Wigner delay times for obliquely incident pulses. The coupling of
evanescent waves to slab plasmon polariton modes results in large traversal
times at the resonant conditions. We also find that the group velocity mainly
contributes to the delay time for pulse propagating across a slab with
refractive index (n) = -1. The traversal times are positive and subluminal for
pulses with sufficiently large bandwidths.
