Radio surveys with the Australia Telescope Compact Array have been carried out at 1.4 and 2.4 GHz with a limiting flux of \sim 0.2 mJy at each frequency in the Marano Field , in which deep optical and X-ray ( ROSAT ) data are also available . In this paper we present the two radio samples , complete at the 5 \sigma _ { local } level , consisting of 63 and 48 sources respectively at 1.4 and 2.4 GHz . The 1.4 GHz normalized differential source counts show a flattening below about one mJy , in agreement with the results from previous surveys . The 2.4 GHz counts , which are the deepest at this or similar frequencies ( e.g . 2.7 GHz ) , agree well with the 2.7 GHz counts at higher fluxes and with the extrapolations down to \sim 2 mJy based on fluctuation analyses . The 2.4–1.4 GHz spectral index distributions are presented for both the complete samples in two flux density intervals . The median spectral index for the 1.4 GHz sample remains constant at \alpha \sim 0.8 , down to the lowest fluxes ( S _ { 1.4 } \simeq 0.2 mJy ) , while for the higher frequency sample the spectral index distribution flattens in the lower flux density interval ( S _ { 2.4 } < 0.8 mJy ) . A significant number of sources with inverted spectrum ( \alpha < 0 ) does appear in both samples , at low flux level ( < \lower 4.558 pt \hbox { $ \kern - 10.7 pt { \sim } $ } 2 mJy ) . These sources , which are about 25 % of the complete sample at 2.4 GHz , are probably the “ bright ” counterpart of the inverted spectrum sources which appear to be almost 50 % of the sources in the even deeper radio surveys ( at \sim 20–40 \mu Jy ) .