The linear absorption and electroabsorption spectra of C60 crystals are discussed theoretically. Excited states of a model cluster consisting of a few C60 molecules are calculated within the extended Pariser-Parr-Pople model and the single-excitation configuration-interaction method. Electroabsorption spectra are numerically calculated by use of the standard formula for the third-order nonlinear optical susceptibility. We assume moderately strong electron-electron interactions and weak interchain transfer energies. The mixing of intermolecular charge transfer components with intramolecular Frenkel exciton states gives rise to weak humps in the tail parts of the main absorption peak. In the electroabsorption spectrum, the charge transfer states have larger contributions than intramolecular excitons. The results are qualitatively in good agreement with experiments.