This paper describes an experimental investigation of dipole-dipole interactions between molecules in an orientationally ordered environment. Measurements are reported of the dielectric properties of a series of anisotropic solutions of two structurally similar dipolar solutes (1-cyano-2-fluoro-4-[trans-4-(trans-4-propylcyclohexyl)cyclohexyl]benzene (CP1) and 1,2-difluoro-4-[trans-4-(trans-4-propylcyclohexyl)cyclohexyl]-benzene (CP3)) dissolved in a nonpolar nematic liquid crystal solvent (1-[trans-4-ethylcyclohexyl]-2-[4-ethyl-2-fluorobiphenyl]ethane (I22)). The solvent provides an orienting medium for the solute molecules, and by varying the temperature the degree of orientational order of the solutions is changed. The measurements have been made on aligned thin films of the liquid crystalline solutions for different concentrations and over a range of frequencies from 1 kHz to 10 MHz. All solutions exhibited a low-frequency relaxation associated with end-over-end reorientation of the polar solutes in the ordered environment. The results indicate that the dipolar interactions in CP1 solutions are qualitatively different from those for CP3 solutions. In particular, the dielectric properties of CP1 solutions can be interpreted by assuming that solute molecules are locally ordered antiferroelectrically, while for CP3 solutions the local order appears to be ferroelectric. Analysis of both the low-frequency permittivities and the dielectric loss supports the interpretation. The results can be fitted to an association model which enables the proportion of parallel and antiparallel species to be determined.