  Aims: Drawing an analogy with Active Galactic Nuclei, we investigate the
one-zone SSC model of Gamma Ray Bursts afterglows in the presence of electron
injection and cooling both by synchrotron and SSC losses. Methods: We solve the
spatially averaged kinetic equations which describe the simultaneous evolution
of particles and photons, obtaining the multi-wavelength spectrum as a function
of time. We back up our numerical calculations with analytical solutions of the
equations using various profiles of the magnetic field evolution under certain
simplifying assumptions. Results: We apply the model to the afterglow evolution
of GRBs in a uniform density environment and examine the impact various
parameters have on the multiwavelength spectra. We find that in cases where the
electron injection and/or the ambient density is high, the losses are dominated
by SSC and the solutions depart significantly from the ones derived in the
synchrotron standard cases.
