Electro-optical experiments on several exciplexes of 9,10-dicyanoanthracene and of N,N-dimethylaniline are reported. It is found that the exciplex fluorescence is polarized parallel to the molecular planes of donor and acceptor. Dipole moments of the fluorescent state are obtained and their relatively small values indicate the pronounced locally excited character of the fluorescent state of these exciplexes. Molecular orbital calculations on the hexamethylbenzene-9,10-dicyanoanthracene exciplex confirm this interpretation. The polarization of the exciplex fluorescence is compared with the polarization of charge-transfer transitions in electron donor-acceptor complexes.