Starburst galaxies generate large-scale winds powered by the activity in the star-forming regions located in the galactic discs. Fragmentation of the disc produced by the outbreak of the wind results in the formation of clouds. Bowshocks caused by the supersonic outflow appear around such clouds. In this paper, we discuss the acceleration of relativistic particles and the production of non-thermal radiation in such scenario. Cosmic rays accelerated at the bowshocks do not reach the highest energies, although the high-energy luminosity generated is significant. We show that up to ∼10 per cent of the gamma-ray emission in starbursts might come from these sources outside the galactic discs. Discrete X-ray sources with a power-law component are also expected.Facultad de Ciencias Astronómicas y GeofísicasInstituto Argentino de Radioastronomía