We present initial results of a comparative near-infrared (NIR) spectroscopic study of the Themis and Veritas asteroid families. These two families are compositionally primitive (mainly Tholen C-types) and likely formed in the same region of the protoplanetary disk. However, their disruption ages are at opposite extremes: 2.5 Gy and 8.3 My, respectively, providing insight into evolutionary processes since their disruption. Our study was motivated in part by the Nesvorny et al. (2005) detection of visible color trends between young and old asteroids families, with these two families at opposite ends of their trend. Our 0.8 to 2.4 micron spectra of four Themis and six Veritas asteroids were obtained using the SpeX instrument on NASA's Infrared Telescope Facility (IRTF). We normalized these spectra using solar analog stars; our reflectance spectra do not exhibit any clear absorption features but they do show a range of slopes. The four Themis family members (older surfaces) have "red” (positive) slopes; in contrast, the six Veritas family members (younger surfaces) have significantly "flatter” slopes (this result includes objects with similar radii so it does not appear to be a function of asteroid size). The clustering of the spectra into two groups with statistically distinct average slopes is consistent with space weathering being a significant modifier of the near-infrared spectral shape of primitive asteroids. In other words, space weathering of primitive asteroids surfaces appears to make them "redder” in the NIR (this work) and less red in the visible (Nesvorny et al. 2005). We gratefully acknowledge support from a Cottrell College Science Award from Research Corporation, and from National Science Foundation and NASA grants.