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The structure of monochromatic MHD-waves with large azimuthal wave number <i>m</i>≫1 in a two-dimensional model of the magnetosphere has been investigated. A joint action of the field line curvature, finite plasma pressure, and transversal equilibrium current leads to the phenomenon that waves, standing along the field lines, are travelling across the magnetic shells. The wave propagation region, the transparency region, is bounded by the poloidal magnetic surface on one side and by the resonance surface on the other. In their meaning these surfaces correspond to the usual and singular turning points in the WKB-approximation, respectively. The wave is excited near the poloidal surface and propagates toward the resonance surface where it is totally absorbed due to the ionospheric dissipation. There are two transparency regions in a finite-beta magnetosphere, one of them corresponds to the Alfvén mode and the other to the slow magnetosound mode.<br><br><b>Key words.</b> Magnetosphere · Azimuthally small-scale waves · MHD waves</p>