The theory of cosmic-ray acceleration by subluminal MHD astrophysical
shocks according to the test particle approximation is extended to hig
hly oblique shocks where flow speeds which appear nonrelativistic in t
he shock rest frame appear on transformation to the de Hoffmann-Teller
or E=0 frame to have upstream flow speeds approaching c. Monte Carlo
simulation shows that relative to the predictions of diffusion theory,
as the upstream E=0 frame velocity approaches c, flatter spectra and
faster acceleration rates occur. These spectral and acceleration time
changes are similar to those found for relativistic, parallel MHD shoc
ks and may affect all nonthermal active galactic nuclei emission from
relativistic electrons. Also there is an additional means of increasin
g the upper limit of the cosmic-ray spectrum expected from active gala
ctic nuclei, although the approximation used may not accurately reprod
uce the spectral shape.