Na1.5Ag1.5MoO3F3 and Na1.5Ag1.5WO3F3 have been synthesized by solid state reactions and structurally characterized using synchrotron X-ray and neutron powder diffraction. Unlike the vast majority of salts containing [MO3F3](3-) anions (M = Mo, W) the oxyfluoride groups in Na1.5Ag1.5MoO3F3 and Na1.5Ag1.5WO3F3 are orientationally ordered, so that the Na+ ions are coordinated by fluorine and the Ag+ ions by oxygen. The resulting structure type, which has not previously been reported, is related to the LiNbO3 structure, but the combination of Na/Ag ordering and orientational ordering of the [MO3F3](3-) anions produces a supercell that doubles the c-axis and changes the space group symmetry from R3 to R (3) over bar. The use of hard (Na+) and soft (Ag+) cations to direct the orientational ordering of polar oxyfluoride building units provides a new approach to the design of polar materials.