We present calculations of the time evolution of the prompt spectra of gamma-ray burst models involving generic internal dissipation regions, including internal shocks, either by itself or in the presence of an external photon source such as a photosphere. The method uses a newly developed time-dependent code involving synchrotron emission and absorption, inverse Compton scattering, and pair formation. The models reproduce the typically observed Band spectra and their generic time evolution, including the appearance of an extra keV–GeV component, whose delay in simple SSC models, however, is only partially able to explain the several seconds observed GeV delays. On the other hand, models involving both a photosphere and an internal dissipation region at a larger radius produce both an extra GeV component and time delays that are in the range of the observations.
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