The equihbrium structure of magnetic fields in stars is investigated assuming the star to be a polytrope and the structure of the field is determined for values of the polytropic index n = 0, 1, 1.5, 2 and 3, using a first order perturbation theory. As the magnetic body force becomes vanishingly small in the surface layers this method is satisfactory. The first three eigen solutions are detennined and it is shown that whereas for n ≤ 1 the number of nodes of the field increases with an increasing ratio of toroidal to poloidal field strength, for n > 1 the field has no nodes between centre and surface, for all values of this ratio.