We model the temporally evolving nonthermal particle and photon spectra at different stages in the lifetime of a standard shell-type supernova remnant. A characteristic νFν spectrum of a SNR consists of a peak at radio-through-optical energies from nonthermal electron synchrotron emission and another high-energy gamma-ray peak due primarily to nonthermal electron bremsstrahlung, Compton scattering, and secondary pion production. We find that SNRs are capable of producing maximum gamma-ray luminosities ≳1034 erg s−1 if the density of the local ISM is ≳1 cm−3. This emission will persist for ≳105 years after the supernova explosion. This long gamma-ray lifetime suggests that SNRs with a wide range of ages could be gamma-ray sources and could constitute some of the unidentified EGRET sources.