In the study of Alfv¿n waves and resonances in the magnetospheres of the Earth and other celestial bodies, orthogonal, magnetic-field-aligned coordinates (OF coordinates) are widely used. Two of the coordinates are constant on field lines, and the direction of the third is parallel to the direction of the ambient magnetic field. In dipolar fields or in nondipolar but still purely meridional axisymmetric fields the existence of such coordinates is evident. OF coordinates, however, are also used occasionally in magnetospheric configurations of more general nontrivial geometry where their existence is far from obvious. In the present paper it is proved that magnetic field configurations cannot support OF coordinates wherever local shear of the magnetic field lines is present. The previously known condition that no field-aligned currents must exist further restricts the admissible geometry of the magnetic field. If the geometry is axisymmetric, a purely meridional or a purely azimuthal magnetic field is the only remaining OF compatible configuration. Therefore publications in which OF coordinates are used together with nontrivial magnetic field configurations need a critical reassessment. ¿ 2000 American Geophysical Union