The results of a previous work, which describes in the magnetohydrodynamic approximation Alfvén wings in nonuniform plasmas, are extended in order to consider more general variations of the background fields. As mathematical tools we use general curvilinear coordinates and stream functions. We prove the possibility of existence of Alfvén wings when the background fields have cylindrical or helical symmetry. For the former, the wings are cylinders, and for the latter, they have helicoidal form; this last includes the case of uniform background fields. We also obtain the relations among the different physical magnitudes in the wing.