[en] The magnetic phase diagram of Dy (T_N=179 K) shows the presence of two phases at elevated fields and temperatures, and these are presumed to be fan structures. Neutron scattering experiments were performed to determine the magnetic structures of these phases at 141, 149 and 172 K with magnetic fields between 0 and 1.8 T. It was found that the structures were characterized by two modulation wave vectors at 141 and 149 K and by only one modulation wave vector at 172 K. As the helical-fan-ferro structural changes occur, the satellite peak intensity shifts to the fundamental peaks. However, the sum of the peak intensities is not conserved because some of this intensity goes into a diffuse component covering a large range of wave vectors. The general features of the data are reproduced by a mean-field and Monte-Carlo calculations. (orig.)