Recent measurements of the reflectance spectra of the nuclei of comets P/Tempel 2 and P/Encke highlight the need for similar spectra of possibly related bodies in the outer solar system. Foremost among these are the Trojan asteroids. Both cometary nuclei and Trojan asteroids have geometric albedos on the order of a few percent, and both groups of objects are known to be elongated relative to main-belt asteroids of comparable size (Jewitt and Meech 1988; Hartmann et al. 1988). We explore the nucleus-Trojan interrelation further by performing a systematic comparison between spectral reflectivities of cometary nuclei and Trojan asteroids. For this purpose, we have obtained high signal-to-noise ratio charge coupled device (CCD) spectra of 32 Trojan asteroids for comparison with the existing cometary nucleus spectra. The Trojan CCD spectra cover the wavelength range 4000≤λ≤7400 Å at 20 Å resolution, with typical signal-to-noise ratios ∼50 per pixel. We find that the reflectivity spectra of Trojan asteroids are characterized by a broad range of linear continuum gradients S′ in the range 3≤S′≤25%/103 Å, with a mean near S′ ∼10%/103 Å. The reflectivity gradients of the comet nuclei fall within the range defined by the Trojan asteroids. In this sense, the optical spectra of the cometary nuclei and of the Trojan asteroids are consistent, enhancing the resemblance between the two groups of objects. Existing photometric and spectral data therefore suggest a remarkable similarity between the Trojans and the nuclei - both are elongated objects, mantled with low albedo, reddish, probably carbon-rich material.