  We have developed a numerical model for the temporal evolution of particle
and photon spectra resulting from nonthermal processes at the shock fronts
formed in merging clusters of galaxies. Fermi acceleration is approximated by
injecting power-law distributions of particles during a merger event, subject
to constraints on maximum particle energies. We consider synchrotron,
bremsstrahlung, Compton, and Coulomb processes for the electrons, nuclear,
photomeson, and Coulomb processes for the protons, and knock-on electron
production. Broadband radio through gamma-ray light curves radiated by
nonthermal protons and primary and secondary electrons are calculated both
during and after the merger event. Using ROSAT observations to establish
typical parameters for the matter density profile of clusters of galaxies, we
find that merger shocks are weak and accelerate particles with relatively soft
spectra. Our results suggest that only a minor contribution to the diffuse
extragalactic gamma-ray background can originate from cluster merger shocks.
