Subcluster interactions within clusters of galaxies produce shocks that accelerate nonthermal particles. We treat Fermi acceleration of nonthermal electrons and protons by injecting power-law distributions of particles during the merger event, subject to constraints on maximum particle energies. The broadband nonthermal spectrum emitted by accelerated electrons and protons is calculated during and following the subcluster interaction for a standard parameter set. The intensity of γ-ray emission from primary and secondary processes is calculated and discussed in light of detection capabilities at radio and γ-ray energies.