  A plausible model for the Crab Nebula is one in which a particle dominated,
highly relativistic wind from the pulsar passes through a shock front in which
the particles attain a power law energy distribution. The electrons and
positrons lose energy radiating synchrotron emission. Here, a one zone version
of the model is developed and applied to observations of X-ray pulsar nebulae.
Efficient conversion of pulsar spin-down power to X-ray luminosity is expected
if the observed electrons are in the synchrotron cooling regime and their
energy spectrum is similar to that in the Crab Nebula. In this case, the
relation between X-ray luminosity and pulsar spin-down power depends only
weakly on the model parameters. The dependence is stronger for a steeper
particle spectrum, as appears to be present in N157B, and the efficiency of
X-ray production can be lower. If the electrons are not in the cooling regime,
the X-ray luminosity can be low, as appears to be the case for the compact
nebula around the Vela pulsar. Slow cooling is likely to be caused by a
sub-equipartition magnetic field in the radiating region. Observations can
place constraints on the uncertain physics of relativistic MHD shocks. The
model is related to those developed for gamma-ray burst afterglows.
