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This article presents results of theoretical and experimental studies on the production of ultrashort (a few RF cycles duration) microwave pulses of gigawatt peak powers based on superradiance from high-current electron beams. With the Cherenkov backward-wave-electron-beam interaction in a low-dispersion slow-wave structure, microwave pulses with a peak power greater than the peak power of the driving electron beam have been produced for the first time. In an experiment using the SINUS-150 compact high-current electron accelerator, with a 2.6-kA injected beam current and a 330-kV electron energy, microwave pulses of 1.2 GW peak power and ∼0.5 ns duration (FWHM) were generated in the X-band. Production of superradiance pulses in a repetitive regime (3500 Hz) in the Ka-band has been demonstrated using a compact hybrid SOS-modulator. The effect of spatial accumulation of microwave energy in extended slow-wave structures with substantially nonuniform coupling has been demonstrated. In an experiment using the SINUS-200 compact accelerator, X-band pulses of ∼3 GW peak power and 0.6-0.7 ns width (FWHM) were produced with a power conversion efficiency of 150-180% and an energy efficiency of ∼15%.