The structure of the rotational low-energy eigenvalue spectrum and eigenfunction of endohedral C 60 fullerene complexes is investigated. The selected systems are Li +@C 60, Na +@C 60, CO@C 60, and LiH@C 60. The eigenvalue spectra may be classified basically into two types. Below some critical degree of anisotropy in the guest-cage interaction the spectrum looks rather simple, and similar to that of an effective diatomic molecule. For high enough anisotropic interactions, the low-energy eigenvalue spectrum is characterized by a double-band structure: a ground band localized around the fullerene hexagon centers, and an excited band embedded in a rotational quasi-continuum and localized at the unstable equilibrium regions around the fullerene pentagon centers. The cage rotation makes the transition from one type to the other much sharper type. Rotation dipole and Raman spectra are assigned in terms of these two types of structure in the eigenvalue spectrum.