We present near-infrared reflectance spectra of two asteroids with low Tisserand invariant, 2906 Caltech and 1373 Cincinnati. The Tisserand invariant is a commonly used dynamical discriminator, with values less than 3 considered suggestive of cometary origin. Asteroids Caltech and Cincinnati have Tisserand invariant values of 2.97 and 2.72 respectively. However, other factors, including their mean orbital intersection distance (MOID) with Jupiter, suggest neither asteroid has a cometary origin. Our spectra covered the 0.8-2.4 micron region and were obtained on UT 22.23 and 23.60 October 2004, using the SpeX instrument at NASA's infrared telescope facility (IRTF) on Mauna Kea. Our reflectance spectra of Caltech and Cincinnati, normalized at 1.22 microns, yield slopes with 17 and 27 percent change in reflectance per micron respectively and display no strong absorption features. The observed red slopes and weak or absent spectral features in the near-infrared are consistent with both the spectra of comet nuclei and of primitive asteroids. We present a detailed spectral comparison of these two asteroids with other comet-asteroid transition objects that are more likely to have a cometary origin, such as 28 P/Neujmin 1 (Licandro et al., 2002), C/2001 OG108 (Abell et al., 2005), 162P/Siding Spring (2004 TU12) and 944 Hidalgo (Campins et al., 2005). References: Abell et al., 2005. Physical Characteristics of Comet Nucleus C/2001 OG108 (LONEOS). Icarus (in press). Campins et al., 2005. Surface Characteristics of Comet-Asteroid Transition Objects 944 Hidalgo and 162P/Siding Spring (2004 TU12). Asteroids Comets Meteors (abstract). Licandro et al., 2002. The Surface of Cometary Nuclei Related Minor Icy Bodies. Earth, Moon, and Planets 90, 495-496.