The X-ray structure of tricaesium deuteriumbiselenate, CS3D(SeO4)2, M(r) = 686.7, has been studied at 25, 190 and 297 K with particular attention being paid to the low-temperature phase transition at T(c3) = 180 K. The structure of Cs3H(SeO4)2 has also been studied at 297 K. The data were refined in the monoclinic space group C2/m, Z = 2, at 297 and 190 K, and in P2(1)/m, Z = 2, at 25 K (Mo Kalpha radiation, lambda = 0.71073 angstrom). For CS3D(SeO4)2, R(F2) = 0.0365 for 1801 unique reflections at 297 K, R(F2) = 0.0389 for 1787 unique reflections at 190 K and R(F2) = 0.0405 for 3514 unique reflections at 25 K. For CS3H(SeO4)2, R(F2) = 0.0637 for 1265 unique reflections at 297 K. Temperature effects on the structure are mainly noticeable in the Cs-O bond distances of the oxygen coordination polyhedra of Cs (0.016 angstrom per 100 K on average). Accompanying the T(c3) transition, the space group changes from C2/m to P2(1)/m, and the two SeO4 groups in the dimer become nonequivalent with one adopting HSeO4- character and the other SeO42- character. As a result, the dimers have a net dipole moment and are arranged in an antipolar way, similar to K3D(SO4)2. An examination of the room-temperature structure of CS3D(SeO4)2 and other M3H(XO4)2-type crystals reveals that the non-H atoms lie in approximately the same position in both cases and that the only major difference is that half of the hydrogens in other M3H(XO4)2-type crystals are involved in hydrogen-bonded dimers which are formed with two different adjacent selenate groups. The successive transitions in Cs3D(SeO4)2 are characterized as an order disorder transition of the donor-oxygen atom at T(c1), reorganization of the hydrogen bonds at T(c2) and an order-disorder transition of the proton at T(c3).