The 3.6 m Canada-France-Hawaii Telescope has been used to study the near-infrared spectrum of the Local Group elliptical M32. The data, which were recorded through a 12 arcsec aperture centered on the galaxy nucleus, span the wavelength range 1.6-2.4 μm with a resolution λ/Δλ∼230 at 2 μm. The strongest features have been identified as absorption bands of CO, CN, and H2O. The 1.8 μm BallikRamsey C2 band head is not conspicuous, suggesting that carbon stars are relatively rare in the nucleus of M32. A suite of model spectra have been constructed using a library of stellar observations, based on evolutionary sequences summarized in The Revised Yale Isochrones and Luminosity Functions (Green et al. 1987). The model spectra consistently underestimate the strengths of the CO bands for a wide range of plausible mass functions, indicating that M32 must contain a population of cool, evolved stars in addition to those evolving on the red giant branch. In an effort to improve the fit to the observations and investigate the nature of the "missing" component, the model spectra were modified by adding spectra of various late-type stars in quantities sufficient to match the strength of the Δv = (2,0) band head of CO. The results imply that the additional component must be dominated by stars later than spectral-type K, which is suggestive of evolution on the asymptotic giant branch (AGB) rather than the horizontal branch. Moreover, it is found that this component must contribute at least 50% of the 2 μm flux, regardless of the assumed stellar content. The model which produces the best fit to the observations, based on the sum of the squares of the residuals, has a relatively steep mass function, and an AGB dominated by late-type M giants and carbon stars, which together produce 60% of the 2 μm flux. This contribution is twice that predicted for an old coeval population, so it is concluded that M32 must contain an intermediate-age population. Finally, the possibility of using near-infrared spectra to study the low-mass dwarf content of M32 and other galaxies is also discussed.