We present near infrared reflectance spectra from 0.8 to 2.5 μm of two asteroids with low Tisserand invariant, 1373 Cincinnati and 2906 Caltech. We compare our spectra with cometary nuclei and other asteroids in their class. Asteroids Cincinnati and Caltech have Tisserand invariant values of 2.72 and 2.97, respectively, values less than 3 are considered suggestive of cometary origin. The observed spectral slopes in the near-infrared are consistent with both the spectra of cometary nuclei and of primitive asteroids. However, both asteroids have features in the near-infrared that are not seen in cometary nuclei, but are present in other X-type asteroids. 1373 Cincinnati has a sharp slope change between 0.75 and 1.0 μm and 2906 Caltech has a broad and shallow absorption between 1.35 and 2.2 μm. Our attempts to model the visible and near-infrared spectrum of these two objects, with the components successfully used by Emery and Brown (2004, Icarus 164, 104 121) to fit Trojan asteroids, did not yield acceptable fits.