Integral equation theories have been quite successful at providing structural information for isotropic fluids. In particular, the expansion method originally proposed by Blum and Torruella [J. Chem. Phys. 56, 303 (1972)] has been pivotal in making these theories feasible for molecular fluids. Recently, integral equation theories have also been applied to nematic phases for simple one-component fluids. In this article, we derive the formalism appropriate for fully, and partially, orientationally anisotropic fluids. Appropriate expansions of the pair and singlet functions are employed to obtain tractable expressions for the three coupled equations which must be solved. The numerical solution of these equations is discussed and simplifications resulting from symmetry are considered in detail. Numerical results are presented for fluids of dipolar ellipsoidal molecules in an external field. (C) 2003 American Institute of Physics.