Assuming that supernova shocks accelerate nonthermal particles, we mod
el the temporally evolving nonthermal particle and photon spectra at d
ifferent stages in the lifetime of a standard shell-type supernova rem
nant (SNR). A characteristic vF(v) spectrum of an SNR consists of a pe
ak at radio through optical energies from nonthermal electron synchrot
ron emission and another high-energy gamma-ray peak due primarily to s
econdary pion production, nonthermal electron bremsstrahlung, and Comp
ton scattering. We find that supernova remnants are capable of produci
ng maximum gamma-ray luminosities greater than or similar to 10(35) er
gs s(-1) if the density of the local interstellar medium is greater th
an or similar to 10 cm(-3). This emission will persist for greater tha
n or similar to 10(5) yr after the supernova explosion because of the
long energy loss timescales for electrons with kinetic energy similar
to 1 GeV. This long gamma-ray lifetime implies that SNRs with a wide r
ange of ages could be gamma-ray sources and could constitute some of t
he unidentified EGRET sources.