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We aim to characterize the nature of galaxies whose optical emission linediagnostics are consistent with star formation, but whose X-ray propertiesstrongly point towards the presence of an AGN. Understanding these sources isof particular importance in assessing the completeness of AGN samples derivedfrom large galaxy surveys, selected solely on the basis of their opticalspectral properties.We construct a large sample of 211 NELGs, which have FWHMsHb emission line <1200 km/s from the SDSS-DR7 galaxy spectroscopic catalogue,for which we are able to construct a classical diagnostic diagram, [OIII]/Hbversus [NII]/Ha (hence z<0.4), and that are also detected in the hard energyband and present in the 2XMM catalogue. This sample offers a large database bywhich to investigate potential mismatches between optical diagnostics and X-rayemission. Among these 211 objects, which based on our selection criteria areall at z<0.4, we find that 145 galaxies are diagnosed as AGNs, having 2-10 keVX-ray luminosities that span a wide range, from 10^40 erg/s to above 10^44erg/s. Out of the remaining 66 galaxies, which are instead diagnosed as SF, wefind a bimodal distribution in which 28 have X-ray luminosities in excess of10^42 erg/s, large T (>1), and large X/O ratio (>0.1), while the rest areconsistent with being simply SF galaxies. Those 28 galaxies exhibit thebroadest Hb line FWHMs, from ~300 to 1200 km/s, and their X-ray spectrum issteeper than average and often displays a soft excess. We therefore concludethat the population of X-ray luminous NELGs with optical lines consistent withthose of a starforming galaxy (which represent 19% of our whole sample) islargely dominated by NLS1s. The occurrence of such sources in the overalloptically selected sample is small (<2%), hence the contamination of opticallyselected galaxies by NLS1s is very small.

The X-ray luminous galaxies optically classified as star forming are mostly narrow line Seyfert 1s