  Radio relic sources in galaxy clusters are often described as the remnants of
powerful radio galaxies. Here we develop a model for the evolution of such
relics after the jets cease to supply energy to the lobes. This includes the
treatment of a relic overpressured with respect to its gaseous surroundings
even after the jets switch off. We also determine the radio emission of relics
for a large variety of assumptions. We take into account the evolution of the
strength of the magnetic field during the phase of relativistic particle
injection into the lobes. The resulting spectra show mild steepening at around
1 GHz but avoid any exponential spectral cut-offs. The model calculations are
used to fit the observed spectra of six radio relics. The quality of the fits
is excellent for {\it all} models discussed. Unfortunately, this implies that
it is virtually impossible to determine any of the important source parameters
from the observed radio emission alone.
