We present reflected light spectral observations from 0.4 to 2.5 μm of 24 asteroids chosen from the population of asteroids initially classified as Tholen X-type objects ( Tholen, 1984). The X complex in the Tholen taxonomy comprises the E, M and P classes which have very different inferred mineralogies but which are spectrally similar to each other, with featureless spectra in visible wavelengths. The data were obtained during several observing runs in the 2004–2007 years at the NTT, TNG and IRTF telescopes. Sixteen asteroids were observed in the visible and near-infrared wavelength range, seven objects in the visible wavelength range only, and one object in the near-infrared wavelength range only. We find a large variety of near-infrared spectral behaviors within the X class, and we identify weak absorption bands in spectra of 11 asteroids. Our spectra, together with albedos published by Tedesco et al. (2002), can be used to suggest new Tholen classifications for these objects. We describe 1 A-type (1122), 1 D-type (1328), 1 E-type (possibly, 3447 Burckhalter), 10 M-types (77, 92, 184, 337, 417, 741, 758, 1124, 1146 and 1355), 5 P-types (275, 463, 522, 909, 1902), and 6 C-types (50, 220, 223, 283, 517, and 536). In order to constrain the possible composition of these asteroids, we perform a least-squares search through the RELAB spectral database. Many of the best fits are consistent with meteorite analogue materials suggested in the published literature. In fact, we find that seven of the new M-types can be fit with metallic iron (or pallasite) materials, and that the low albedo C/P-type asteroids are best fitted with CM meteorites, some of which have been subjected to heating episodes or laser irradiation. Our method of searching for meteorite analogues emphasizes the spectral characteristics of brightness and shape, and de-emphasizes minor absorption bands. Indeed, faint absorption features like the 0.9 μm band seen on four newly classified M-type asteroids are not reproduced by the iron meteorites. In these cases, we have searched for geographical mixture models that can fit the asteroid spectrum, minor bands, and albedo. We find that a few percent (less than 3%) of orthopyroxene added to iron or pallasite meteorite, results in good spectral matches, reproducing the weak spectral feature around 0.9 μm seen on 92 Undina, 417 Suevia, and 1124 Stroobantia. For 337 Devosa, a mixture model that better reproduces its spectral behavior and the 0.9 μm feature is made with Esquel pallasite enriched with goethite (2%). Finally, we consider the sample of the X-type asteroids we have when we combine the present observations with previously published observations for a total of 72 bodies. This sample includes M and E-type asteroid data presented in Fornasier et al. (2008, 2010). We find that the mean visible spectral slopes for the different E, M and P Tholen classes are very similar, as expected. An analysis of the X-type asteroid distribution in the main belt is also reported, following both the Tholen and the Bus–DeMeo taxonomies ( DeMeo et al., 2009).