  The EGRET supernova remnants (SNR's) are all expanding into nearby dense
molecular clouds, powering a shock at the interface where protons and electrons
accelerate to relativistic energies. A viable mechanism for the emission of
gamma$-rays in these sources is the decay of neutral pions created in
collisions between the relativistic hadrons and protons in the ambient medium.
But neutral pion decay alone cannot reproduce the whole high-energy spectrum,
particularly below 100 MeV. A pion-decay scenario thus requires a lepton
population to "fill in" the lower part of the spectrum via bremsstrahlung
emission. This population, however, is constrained by the SNR radio spectrum.
Taking our cue from the behavior of Sgr A East, an energetic EGRET SNR at the
Galactic center, we here examine the role played in these sources by secondary
leptons--electrons and positrons produced in proton-proton scattering events
and the ensuing particle cascades. We show that while secondary leptons cannot
account for the gamma-rays below 100 MeV, they can account for the hard radio
spectra observed from the EGRET SNR's. Thus, it appears that both primary and
secondary leptons may be important contributors to the overall broadband
emission from these sources, but if so, must radiate most of their energy in
different parts of the SNR-cloud environment. We show that shock acceleration
in dense cores being overtaken by the expanding SNR shell can naturally lead to
such a scenario.
