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Gamma-ray bursts (GRBs) are the phenomena of rapid energy release of enormous power associated with the collapse or merging of stars. As a result of internal processes, populations of nonthermal accelerated particles radiating in a wide energy range are formed in them. A number of observations have shown that photons with energies up to tens of TeV are detected from some GRBs. However, due to the great energy losses of radiating particles, the explanation of this high-energy radiation in terms of standard radiation mechanisms runs into great difficulties. In this paper, based on the model of adiabatic expansion for the GRB afterglow phase, we investigate the influence of magnetic inhomogeneities on the spectra within the electron and proton synchrotron radiation mechanism by taking into account the Compton scattering of synchrotron photons. We show that the magnetic inhomogeneity effect can increase the maximum energies of the synchrotron radiation from electrons and protons several fold without affecting the maximum energies of the Compton photons being produced in the Klein–Nishina regime. [ABSTRACT FROM AUTHOR]