The problem of a source moving in a plasma with background fields varying in one direction, in the magnetohydrodynamic approximation, is analyzed. The variation of the background fields is assumed to be perpendicular to the background velocity and induction magnetic fields. Since Alfv¿n wings are closely related to Alfv¿n waves, the existence of Alfvenic perturbations, in this case, is searched. Instead of linearizing the MHD equations and searching monochromatic waves, the conditions that the group velocity be parallel to the background magnetic induction field, in the reference system in which the plasma is locally at rest, the perturbation be incompressible, and the total pressure remain constant, are imposed. Two modes of propagation are found. Since it is possible to define an invariant direction, the methodology of stream functions is used for the analysis of Alfv¿n wings. Their existence, when the variation of the background fields satisfies some conditions, is proved, and the relations among the density, pressure, magnetic field, plasma velocity, and electric current density in the wing are found. Physical situations in which these results can be applied, with such a particular spatial dependence of the background fields, are restricted. However, as an approximation, it can be applied to spacecraft or space tethers moving in a circular orbit, if one takes into account that the density and the induction magnetic field change with the altitude. The method can be extended to cases in which the background fields vary in a more general way. ¿ 2000 American Geophysical Union