We present a theory for modeling fluorescence-detected two-dimensional electronic spectroscopy of multichromophoric systems. The theory is tested by comparison of the predicted spectra of the light-harvesting complex LH2 with experimental data. A qualitative explanation of the strong cross-peaks as compared to conventional two-dimensional electronic spectra is given. The strong cross-peaks are attributed to the clean ground-state signal that is revealed when the annihilation of exciton pairs created on the same LH2 complex cancels oppositely signed signals from the doubly excited state. This annihilation process occurs much faster than the nonradiative relaxation. Furthermore, the line shape difference is attributed to slow dynamics, exciton delocalization within the bands, and intraband exciton-exciton annihilation. This is in line with existing theories presented for model systems. We further propose the use of time-resolved fluorescence-detected two-dimensional spectroscopy to study state-resolved exciton-exciton annihilation.