  Starburst galaxies generate large-scale winds powered by the activity in the
star-forming regions located in the galactic disks. Fragmentation of the disk
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% of the gamma-ray
emission in starbursts might come from these sources outside the galactic
disks. Discrete X-ray sources with a power-law component are also expected.
