Aims:We have investigated the spectral properties of the E-type asteroids 2867 Steins, a main belt object target of the Rosetta mission, and 3103 Eger, a near Earth asteroid. The strong spectral similarity between these two objects suggests a possible common origin in spite of their presently different orbits. We explore the possibility that Steins and Eger are both remnants of an old asteroid family, the outcome of the breakup of a parent body at about 2.36 AU. Eger possibly moved into an Earth-crossing orbit driven by the Yarkovsky effect and resonances. Methods: Low resolution spectroscopy in the visible range was carried out with the 3.5 m New Technology Telescope (NTT) of the European Southern Observatory. We used the numerical integrator SWIFT-RMVSY, which takes into account the diurnal and seasonal Yarkovsky effect, to simulate the dynamical evolution of fictitious family fragments. Results: The spectra of Steins and Eger are very similar, and both show an absorption feature centered at 0.49 μm typical of the E[II] subgroup. They are peculiar among the subgroup because of the deep absorption feature and steep spectral slope. They may be members of an old eroded asteroid family which formed close to the present location of Steins. Numerical orbital integrations show that there is a dynamical pathway between the present orbit of Steins, possibly the largest remnant of the family, and Earth-crossing orbits like that of Eger. Based on observations carried out at the European Southern Observatory (ESO), La Silla, Chile, ESO proposal 076.C-0047 and 078.C-0115.