of magnitude less than the magnetic field of the wind. High-energy electrons which are accelerated at the wind front and injected into the region ahead of the front generate synchro-Compton radiation in the fields of large-amplitude electromagnetic waves. This radiation closely resembles synchrotron radiation and can reproduce the non-thermal radiation of $\gamma$-ray bursts observed in the Ginga and BATSE ranges (from a few keV to a few MeV). Synchrotron photons which are generated in the vicinity of the wind front may be responsible for the radiation of $\gamma $-ray bursts in the EGRET energy range above a few ten MeV. The spectrum of $\gamma$-ray bursts in high-energy $\gamma$-rays may extend, in principle, up to the maximum energy of the accelerated electrons which is about $10^{13}(\Gamma_0/10^2)^2$ eV in the frame of the $\gamma$-ray burster.'
author:
- 'M.V. Smolsky and V.V. Usov'
title: 'Non-thermal radiation of cosmological $\gamma$-ray bursters'
---

Introduction {#Introduction}
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Many ideas about the nature of $\gamma$-ray bursts have been discussed during last 25 years after their discovery (for a review, see [@Blaes94]; [@Harding94]; [@Hartman95]; [@Dermer95]; [@FM95]; [@Greiner98]; [@Piran98]). Among these ideas, there was a suggestion that the sources of $\gamma$-ray bursts (GRBs) are at cosmological distances, i.e. at 