Rotational line strength expressions are derived forn-photon transitions between two multiplet states of diatomic molecules which both belong to coupling cases that are intermediate between Hund's case (a) and case (b). Rotational selection rules forn-photon transitions are given. For doublet states, rotational line strengths are given in terms of coupling parameters, states with any multiplicity may be treated in the same way. Different kinds of transitions are discussed.