The electromagnetic interaction energy of a molecular aggregate consisting of pointlike molecules in the presence of an electromagnetic field is derived. The corresponding Hamiltonian consists of three parts; H-0 describes the aggregate in the absence of the electromagnetic field, H-1 describes the interaction of the molecules with the external field, and H-2 corresponds to the induced interaction between the molecules. Based on this Hamiltonian we derive a self-consistent equation of motion for a quasiparticle, which we refer to as a polarized exciton. The equation has the same form as the one in classical dipole theory. The polarized exciton model is based on a time-dependent perturbative treatment and corresponds to the assumption H-0 much greater than H-1 + H-2. Our model is compared to standard exciton theory, which is based on the assumption H-0 much greater than H-2 much greater than H-1. In particular the differences and similarities are illustrated for a direct example, a finite linear chain. We advocate the use of polarized excitons to fully account for the physics in these systems. (C) 2001 American Institute of Physics.