a redshift $z\sim 1$ ([@Usov75]; [@vdBerg83]; [@Paczynski86]; [@Goodman86]; [@Eichler89]). After the BATSE data became available ([@Meegan92], 1994), the idea of a cosmological origin of GRB sources has come to be taken very seriously (e.g., [@Paczynski91]; [@FM95]). Recent detections of absorption and emission features at a redshift $z=0.835$ in the optical afterglow of GRB 970508 ([@Metzger97]) and at redshift $z=3.42$ in the host galaxy of GRB 971214 ([@Kulkarni98]) clearly demonstrate that at least some of the GRB sources lie at cosmological distances. A common feature of all acceptable models of cosmological $\gamma$-ray bursters is that a relativistic wind is a source of GRB radiation. The Lorentz factor, $\Gamma_0$, of such a wind is about $10^2-10^3$ or even more (e.g., [@Fenimore93]; [@Harding97]). A very strong magnetic field may be in the plasma outflowing from cosmological $\gamma$-ray bursters ([@Usov92], 1994a,b; [@Thompson93]; [@Blackman96]; [@Vietri96]; [@Katz97]; [@Meszaros97]; [@Dai98]). It was pointed out ([@Meszaros92], 1993; [@Rees92]) that the kinetic energy of relativistic winds may be converted into non-thermal radiation of GRBs when these winds interact with an ambient medium (e.g., an ordinary interstellar medium or plasma which is ejected from the predecessor of the burster). Recently, the interaction between a relativistic magnetized wind and an ambient 