We report Giant Metrewave Radio Telescope (GMRT) continuum observations of six nearby normal galaxies at 333 MHz. The galaxies are observed with angular resolutions better than ∼20 arcsec (corresponding to a linear scale of about 0.4–1 kpc). These observations are sensitive to all angular scales of interest, since the resolution of the shortest baseline in GMRT is greater than the angular size of the galaxies. Furthermore, for five of these galaxies we show that at 333 MHz, the mean thermal fraction is less than 5 per cent. Using archival data at about 1 GHz, we estimate the mean thermal fraction to be about 10 per cent at that frequency. We also find that the non-thermal spectral index is generally steeper in regions with low thermal fraction and/or located in the outer parts of the galaxy. In regions of high thermal fraction, the non-thermal spectral index is flatter, and has a narrow distribution peaking at ∼−0.78 with a spread of 0.16, putting stringent constraints on the physical conditions for generation, diffusion and energy losses of cosmic ray electrons at scales of ∼1 kpc.