We performed a high-sensitivity search for galaxy-scale magnetic fields by radio polarimetry at 10.45GHz and 4.85GHz with the Effelsberg 100m radio telescope, accompanied by Halpha imaging, for the two Local Group irregular galaxies IC10 and NGC6822. Their star-forming bodies are small and rotate slowly. IC10 is known to have a very high star-forming activity, resembling blue compact dwarfs, while NGC6822 has a low overall star-formation level. Despite very different current star formation rates, our Halpha imaging revealed a large web of diffuse Halpha filaments and shells in both IC10 and NGC6822. Some of them extend far away from the galaxy's main body. The total power emission of both objects shows bright peaks either at the positions of optically strong star-forming clumps (IC10) or individual HII regions or supernova remnants (NGC6822). However, in both cases we detect a smoothly distributed, extended component. In IC10 we found clear evidence for the presence of a diffuse, mostly random magnetic field of ~14muG strength, probably generated by a fluctuation dynamo. One of the Halpha-emitting filaments appears to be associated with enhanced magnetic fields. We also rediscuss the reddening of IC10 and its implications for its distance. In the case of NGC6822 we found only very weak evidence for nonthermal emission, except perhaps for some regions associated with local gas compression. We detect in both galaxies small spots of polarized emission, indicative of regular fields (~3muG), at least partly associated with local compressional phenomena.

accepted for publication in AA, 13 pages including 10 figures, high-res version at http://www.oa.uj.edu.pl/~chris/publ/ic10.ps.gz