a b s t r a c tThe structural and vibrational properties of SrHfO 3 compared to those of the SrZrO 3 were investigated using first-principles calculations. The phonon dispersion curves, reported in the high-symmetry cubic perovskite phase, point out the coexistence of structural antiferrodistortive instabilities at the R and M zone-boundary points and a ferroelectric instability at the zone center. Different possible intermediate phases are characterized by comparing their internal energies, giving the same hierarchy of phases as for the SrZrO 3 . The main features of the ferroelectric instability are also discussed, and, contrary to what was found for SrZrO 3 , it seems very unlikely to induce the ferroelectricity in the SrHfO 3 Pnma ground state either by compressive or tensile epitaxial strain.