\neq 0)$ or perpendicular $(\vartheta \neq \pi /2)$, there are at least two regions where powerful non-thermal X-ray and $\gamma$-ray emission of GRBs may be generated. The first region is at $r \sim r_f \sim 10^{13}-10^{14}$ cm, and the second one is at $r\sim r_{\rm dec}\sim 10^{16}- 10^{17}$ cm. Acceleration of electrons and their radiation in the first radiating region at $r\sim r_f$ were considered in details earlier (Usov 1994a,b; Blackman et al. 1996; Blackman & Yi 1998). Below, we consider the spectrum of electrons accelerated at $r\sim r_{\rm dec}$ and their radiation.

Interaction of a relativistic strongly magnetized wind with an ambient medium {#interaction}
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For consideration of the interaction between a relativistic magnetized wind and an ambient medium, it is convenient to switch to the co-moving frame of the outflowing plasma (the wind frame). While changing the frame, the magnetic and electric fields in the wind are reduced from $B$ and $E=B[1-(1/\Gamma_0^2)]^{1/2}
\simeq B$ in the frame of the $\gamma$-ray burster to $B_0\simeq B/\Gamma_0$ and $E_0=0$ in the wind frame. Using this and equation (\[Bdec\]), for typical parameters of cosmological $\gamma$-ray bursters (see § 2) we have $B_0\simeq 10^2-10^3$ G at $r\simeq r_{\rm dec}$.

In the wind frame, 