Compton scattering of the microwave background photons by beams of ultrarelativistic electrons at large redshifts, z >> 1, is proposed as a source of some gamma-ray bursts. Such beams may be produced by cusps on superconducting cosmic strings. In our model a very narrow beam of ultrarelativistic electron-positron pairs scatters the microwave background photons into a very narrow beam of gamma rays. While the pairs lose energy, the beam of gamma rays opens up and sweeps the observer. The expected time variability and spectra of the resulting gamma-ray burst are calculated. The bursts have a rapid rise time, followed by a more gradual decline. The spectra are initially very hard and become softer during the decline. The limits imposed by the energy density of the microwave background allow bursts with a fluence as high as 10^-5^ ergs cm^-2^, and a rise time as short as 10 ms from sources at redshifts as large as z = 10^2^-10^3^.
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Zdziarski et al. (1991) studied this question.