Polycrystalline DyNi₂B₂C samples, as-cast and annealed, were prepared and studied by x-ray diffraction (indicating the LuNi₂B₂C-type structure) and by magnetization. The magnetization study (in H = 20 Oe) of both samples indicates initial ordering at T_N = 16.3(3) K, and a second transition, especially in the annealed one, at T_o = 10.4(3) K. Transitions into superconducting states occur at T_c6 K in the annealed sample and at higher T_c in the as-cast sample. The two magnetic transitions agree with available neutron-diffraction data on annealed polycrystalline DyNi₂¹¹B₂C. A two-step magnetic ordering is proposed, involving initial ferromagnetic order in the basal planes, followed by a build-up of the correct antiferromagnetic (alternate) stacking of these planes throughout the samples. It is completed at the lower transition, T_o, only in the annealed sample, leading to its lower T_c.