Using the full-potential linearized augmented-plane-wave (FLAPW) method, the mechanism of the rutile-CaCl₂ phase transition of RuO₂ and the phase stability of β-PtO₂ are investigated. The local density functional calculations predict quantities such as lattice constants, bulk moduli, and phonon frequencies in good agreement with experiment. The pressure-induced phase transition in RuO₂ appears to be driven by the strong repulsion between O-O and Ru-O along the diagonal direction in the xy-plane. By contrast, a strong hybridization between the Pt 5d and O 2p states is responsible for the stability of the β-PtO₂ structure, for which a pseudo-gap (instead of the strong peak for the rutile-PtO₂) is opened at the Fermi level due to the rotation of the PtO₆ octahedra.