The high-temperature structures of SrZrO 3 have been determined by neutron powder profile refinement, and the phase transitions described by the condensation of soft vibrational modes. At 900°C, SrZrO 3 is tetragonal, I4/mcm, with an O octahedron antiphase tilt of 6.5 ° about [001], intermediate between those found in the isomorphous phases of SrTiO 3 below 110 K and KMnF 3 below 184 K. At 760°C the structure is orthorhombic Bmmb with almost equal b o and c o axes, and not tetragonal. In addition to the antiphase tilt, now 8.5 ° about 1001 I, there is an in-phase tilt of 3.1 ° about [0101. Yet a third tilt, antiphase about 1100] and identical to that about [001], is introduced at room temperature. This series of transitions indicates that the sequence of condensation of soft modes from the high-temperature cubic phase is R25, M a and finally R25 again. In addition, the two latter transitions are first order, and are accompanied by a condensation from the X-point of the Brillouin zone, which produces atomic displacements. The unusually anisotropic thermal ellipsoids provide some additional evidence for the existence of low-frequency vibrational modes.