Photosynthetic organisms have developed antenna systems to enlarge their cross section for capturing sunlight. These systems involve in some cases aggregates of bacteriochlorophylls (BChls). The structure of one such aggregate, a tightly coupled circular hexadecamer of BChls and a loosely coupled octamer of BChls, has recently been solved. In this paper we investigate the electronic excitations in these two aggregates as well as in monomeric BChl and BChl dimers by means of INDO/S-CI calculations. The results provide a detailed description of the properties of electronic states in the BChl aggregates (energies, dipole and transition dipole moments) that are relevant for the biological function of BChls, to absorb light and transfer energy on the subpicosecond time scale. The lower-energy excitations of the BChl hexadecamer are of exciton type, i.e., experiencing a strong coupling that leads to excitation delocalization over the entire aggregate. An effective Hamiltonian is provided which reproduces these exciton states and which can be readily generalized to other aggregates.