X-ray luminous narrow emision-line galaxies (NELG) have been previously identified and proposed as an important class of extragalactic X-ray source, with a potentially significant contribution to the total extragalactic X-ray flux at energies below ∼ 10 keV. In order to investigate and clarify this possibility, we have used a sample of NELG found in 5 deep ROSAT fields and similar samples belonging to the CambridgeCambridge ROSAT Serendipity Survey and to the Einstein Observatory Extended Medium Sensitivity Survey sample. We have been able to study their X-ray properties, to derive their number-flux relationship, to investigate their cosmological evolution and to derive a preliminary X-ray luminosity function (XLF) for this class of objects. We have compared the above mentioned properties to those exhibited by soft Xray selected Broad Line AGN (BLAGN) and/or normal galaxies. The principal results of this investigation are as follows: a) for a given optical luminosity, the typical X-ray luminosity of NELGs is about one or two orders of magnitude higher than that of normal galaxies; b) the ratio of the surface density of NELGs compared with BLAGN increases from∼ 0.04 at fx >∼ 6×10 −13 ergs cm secto∼ 0.1 at fx >∼ 10 −14 ergs cm sec, suggesting that the surface density of NL galaxies might be very close to that of BLAGN at fx ∼ 10 −15 ergs cm sec; c) we find that these objects are described by a cosmological evolution rate similar to that of soft X-ray selected BLAGN; d) the de-evolved (z = 0) XLF of NELGs in the luminosity range 10 − 5 × 10 ergs secis steeper than the BLAGN (z = 0) XLF in the same luminosity interval. Their spatial density is significantly lower than the spatial density of X-ray selected BLAGN at Lx(z = 0) ∼ 5× 10 43 ergs sec, but this difference decreases at lower luminosities such that at Lx(z = 0) ≤ 10 42 ergs secthe spatial density of NELGs is very close to that of BLAGN. The implications of these results for the contribution of this class of objects to the cosmic X-ray background are discussed.