Element specific x-ray resonant magnetic scattering (XRMS) investigations were undertaken to determine the magnetic structure of the multiferroic compound, hexagonal DyMnO₃. In the temperature range from 68 K down to 8 K the Dy3+ moments are aligned and antiferromagnetically correlated in the c direction according to the magnetic representation Γ₃. The temperature dependence of the observed intensity can be modeled assuming the splitting of ground-state doublet crystal-field levels of Dy3+ by the exchange field of Mn3+. XRMS together with magnetization measurements indicate that the magnetic representation is Γ₂ below 8 K.