In terms of a three-dimensionally inhomogeneous model of the magnetosphere, we have investigated theoretically the process of propagation across the geomagnetic field of monochromatic standing Alfven waves that are transversally small-scale ones. For this purpose we introduced an orthogonal coordinate system tied in a natural manner to the geomagnetic field. It is shown that a three-dimensionally inhomogeneous magnetosphere is composed of sectors that differ from each other by the propagation character of the waves with a different sign of azimuthal wave number. The study revealed the existence of transversally small-scale waves produced near the toroidal surface in one sector and absorbed near this same surface in another sector of the magnetosphere. These phenomena have no analog in the theory of the axisymmetric magnetosphere where oscillations come into being near the poloidal surface and propagate toward the toroidal surface. ¿ American Geophysical Union 1995