Drift-mode stability analysis for the Tandem Mirror Experiment is formulated assuming MHD-stability from magnetic field curvature and plasma rotation. The self-consistent field equations describe two potentially unstable drift modes. For k|| ∼ 2π/Lc, where Lc is the length of the central cell, the electron drift wave occurs with ω ∼ ω*eS(b, ηi) ∼ k||vA with a radial localization to the region of maximum electron diamagnetic drift frequency ω*e. For flute-like axial modes, the ion drift wave ω ∼ ω*i > k||vA occurs. The ion drift mode is less radially localized and extends to high frequencies for large k⊥ρi. Stability conditions as a function of ηi, ηe, β and Ti/Te are developed for the drift modes including the guiding-centre drifts and bounce frequency resonances with the electrons.