  Pulsar wind driven synchrotron nebulae are offering a unique view on the
connection of the pulsar wind and the surrounding medium. The Crab nebula is
particularly well suited for detailed studies of the different emission
regions. As inferred from the observed synchrotron emission extending beyond
MeV energies, the Crab is a unique and extreme accelerator. In the framework of
the synchrotron/inverse Compton emission model, the same electrons with
energies exceeding $10^{15}$ eV that are responsible for the MeV synchrotron
emission produce via inverse Compton scattering 10-50 TeV radiation which has
recently been observed with the HEGRA system of ground based gamma-ray
telescopes. Here we discuss the close relation of the two energy bands covered
by INTEGRAL and ground based gamma-ray telescopes. Despite the lack of
sufficient spatial resolution in both bands to resolve the emission region,
correlation of the flux measurements in the two energy bands would allow to
constrain the structure of the emission region. The emission region is expected
to be a very compact region (limited by the life-time of the electrons) near
the termination shock of the pulsar wind. We extend previous model calculations
for the nebula's emission to include an additional compact non-thermal emission
region recently detected at mm wavelengths.The overall good agreement of this
model with data constrains additional emission processes (ions in the wind,
inverse Compton from the unshocked wind) to be of little relevance.
