In the framework of ground-based science campaign dedicated to the encounter with Rosetta spacecraft, the mineralogies of the asteroids (21) Lutetia and (2867) Steins were investigated. Near-infrared (NIR) spectra of the asteroid in the 0.8–2.5 μm spectral range have been obtained with SpeX/IRTF in remote-observing mode from Meudon, France, and Cambridge, MA, in March, April and December 2006 and in January and March 2007. A χ2 test using meteorite spectra from the RELAB database was performed in order to find the best fit of complete visible+infrared (VNIR) spectra of Lutetia. To constrain the possible composition of Steins’ surface, we constructed a simple mixing model using a linear (areal) mix of three components obtained from the RELAB database. A space-weathering model was applied to the aubrite ALH-78113 spectrum. In the case of (21) Lutetia we find a clear spectral variation (slope), and a good correspondence between spectral variations and rotational phase. The surface mixing model places Steins in a subdivision of the E-type class with objects like Angelina, Eger, and Nereus, a group not sampled by the current collection of aubrite meteorites. [ABSTRACT FROM AUTHOR]