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Drift-mirror modes in a one-dimensional inhomogeneous model of the magnetosphere are studied by employing gyrokinetics, taking into account finite Larmor radius effects. A wave equation is derived which describes both the spatial structure of the modes, and its eigenvalue yields a growth rate of the mode. The finite Larmor radius effects are shown to raise the instability threshold especially for high-<i>m</i> waves, and lead to wave propagation across field lines.