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We present ASCA GIS observations (total exposure 100-200 ksec) of threefields which form part of our deep ROSAT survey. We detect 26 sources down to alimiting flux (2-10 keV) of 5x10^{-14} erg cm-2 s-1. Sources down to this fluxlevel contribute 30 per cent of the 2-10 keV X-ray background. The number-countdistribution, logN-logS, is a factor of three above the ROSAT counts, assuminga photon spectral index of 2 for the ROSAT sources. This suggests the presenceat hard energies of a population other than the broad-line AGN which contributeto the ROSAT counts. This is supported by spectroscopic observations that showa large fraction of sources that are not obvious broad-line AGN. The average1-10 keV spectral index of these sources is flat (0.92+-0.16), significantlydifferent than that of the broad-line AGN (1.78+-0.16). Although some of theNarrow Emission Line Galaxies which are detected with ROSAT are also detectedhere, the nature of the flat spectrum sources remains as yet unclear.Comment: 8 pages, Latex. To appear in MNRA

ASCA observations of deep ROSAT fields -- I. The nature of the X-ray source populations