ESR properties of coherent triplet excitons moving between the differently oriented molecules of a nonresonant AB pair in a crystal of the anthracene type are investigated. The model Hamiltonian contains the different electronic excitation energies of the molecular pair, the electronic transfer integral, the Zeeman energy of the triplet spin in an external magnetic field, and the fine structure interactions at the two differently oriented molecules of the pair. As a function of the strength and orientation of the external magnetic field energy eigenvalues, ESR transition energies and transition probabilities for microwave fields orthogonal and parallel to the static magnetic field are calculated analytically in the high field case. The relations of the theoretical results to experimentally observable quantities are discussed. © 1982 American Institute of Physics.