We describe spectroscopy measurements of double wall carbon nanotubes using a displacement photocurrent technique. Peaks in the photocurrent are observed at excitation energies corresponding to the spacing of van Hove singularities for both the inner and outer shells of the nanotube. The shell assignment for the peaks can be made by comparing the spectra before and after the formation of the inner shell. The level spacing observed for the inner shell suggests that the standard tight binding model is insufficient to describe the electron energy spectra for extremely small tubes. (c) 2005 Elsevier B.V. All rights reserved.