A theory for the calculation of resonant and nonresonant hole-burning (HB) spectra of pigment-protein complexes is presented and applied to the water-soluble chlorophyll-binding protein (WSCP) from cauliflower. The theory is based on a non-Markovian line shape theory ( Renger and Marcus J. Chem. Phys. 2002 , 116 , 9997 ) and includes exciton delocalization, vibrational sidebands, and lifetime broadening. An earlier approach by Reppert ( J. Phys. Chem. Lett. 2011 , 2 , 2716 ) is found to describe nonresonant HB spectra only. Here we present a theory that can be used for a quantitative description of HB data for both nonresonant and resonant burning conditions. We find that it is important to take into account the excess energy of the excitation in the HB process. Whereas excitation of the zero-phonon transition of the lowest exciton state, that is, resonant burning allows the protein to access only its conformational substates in the neighborhood of the preburn state, any higher excitation gives the protein full access to all conformations present in the original inhomogeneous ensemble. Application of the theory to recombinant WSCP from cauliflower, reconstituted with chlorophyll a or chlorophyll b, gives excellent agreement with experimental data by Pieper et al. ( J. Phys. Chem. B 2011 , 115 , 4053 ) and allows us to obtain an upper bound of the lifetime of the upper exciton state directly from the HB experiments in agreement with lifetimes measured recently in time domain 2D experiments by Alster et al. ( J. Phys. Chem. B 2014 , 118 , 3524 ).