In this paper we report first optical reflectance spectra in the wavelength range 3800--9000 \AA\ for seven members of the Veritas asteroid family, as determined by Zappal\`a {\em et al.} (1994, {\em Astron. J.}, {\bf 116}, 291--314). The observed asteroids are 490 {\em Veritas}, 844 {\em Leontina}, 1086 {\em Nata}, 2428 {\em Kamenyar}, 2934 {\em Aristophanes}, 5592 {\em Oshima}, and {\em 1985 TQ$_{1}$}. In addition, we observed also the object 5107 {\em 1987 DS$_{6}$}, which joins the Veritas family when a slightly more relaxed criterion of selection is adopted. The obtained spectra show a surprising slope gradient spanning from 0 to about 8\%, a range which includes the slopes characteristics of all the low albedo, primitive bodies (from C to D--type). Taking into account the very compact structure of the family -- the probability of finding interlopers inside the defined clustering is practically zero --, this result seems to confirm the suggestion by Vilas and Sykes (1996, {\em Icarus}, in press) about the presence of thermally altered large asteroids inside the outer belt population. However, the hypothesis of possible space weathering processes cannot completely ruled out. A tentative representation of the post--impact velocity field has been also obtained, showing a possible peculiar ejection of the fragments.