Crystal structures for the fluorite-related phases CaHf4O9 ф1) and Ca6Hf19O44 (ф2) have been determined from X-ray powder diffraction data. qf1 is monoclinic, C2c, with a = 17.698 Å, b = 14.500Å, c = 12.021 Å, β = 119.47° and Z = 16. qf2 is rhombohedral, R3c, with a = 12.058 Å, α = 98.31° and Z = 2. Both phases are superstructures derived from the defect fluorite structure by ordering of the cations and of the anion vacancies. The ordering is such that the calcium ions are always 8-coordinated by oxygen ions, while the hafnium ions may be 6-, 7-, or 8-coordinated. The closest approach of anion vacancies is a 12〈111〉 fluorite subcell vector, and in each structure vacancies with this separation form strings.