The effect of the anisotropic pressure of a hot‐electron plasma on ballooning‐interchange and compressional‐Alfve´n modes is investigated. General eigenmode equations for these modes are derived in the eikonal and high phase velocity limits with finite gyroradius effects retained. A local dispersion relation is obtained in the flute limit for an isotropic Maxwellian background plasma with a bi‐Maxwellian hot‐electron population. Stability is investigated both analytically and numerically for this high phase velocity and/or high precessional frequency model.