Hard X-ray and gamma-ray emission is expected from supernova remnants due t
o synchrotron radiation, nonthermal bremsstrahlung, decay of neutral pions
produced by cosmic ray protons and ions colliding with thermal gas, and inv
erse-Compton emission from relativistic electrons upscattering cosmic micro
wave background photons. The question of the maximum energy to which partic
les can be accelerated by shocks is of great astrophysical interest, and th
e identification of hard X-ray synchrotron radiation gives direct evidence
for electrons of energies of order 100 TeV and higher. Bard X-rays can also
be produced by bremsstrahlung from nonrelativistic but superthermal electr
ons that form the low-energy end of the accelerated-particle spectrum. Dete
ction of remnants in TeV gamma rays requires the presence of 100 TeV electr
ons. Another discriminant is possible with spectra and images in hard X-ray
s. The IBIS imager on INTEGRAL will be able to localize X-ray emission well
enough to distinguish synchrotron and nonthermal radiation in the remnant
of SN 1006 between 15 and 50 keV. I exhibit model images and spectra of syn
chrotron radiation and nonthermal bremsstrahlung for a variety of model par
ameters.