[en] The field-induced magnetic structures of ErNi₂B₂C and TmNi₂B₂C in are especially interesting because the field suppresses the superconducting order parameter and therefore the magnetic properties can be studied while varying the strength of superconductivity. ErNi₂B₂C: For magnetic fields along all three symmetry directions, the observed magnetic structures have a period corresponding to the Fermi surface nesting structure. The phase diagrams present all the observed magnetic structures. Two results remain unresolved: 1. When applying the magnetic field along [010], the minority domain (Q_N^B = (0,Q,0) with moments perpendicular to the field) shows no signs of hysteresis. I expected it to be a meta-stable state, which would be gradually suppressed by a magnetic field, and when decreasing the field it would not reappear until some small field of approximately 0.1 T. 2. When the field is applied along [110], the magnetic structure rotates a small angle of 0.5 degrees away from the symmetry direction. TmNi₂B₂C: A magnetic field applied in the [100] direction suppresses the zero field magnetic structure Q_F = (0.094,0.094,0) (T_N = 1.6 K), in favor of the Fermi surface nesting structure Q_N = (0.483,0,0). The appearance of the Q_N phase was initially believed to be caused by the suppression of superconductivity. This suppression should make it favorable to create a magnetic order with a Q-vector determined by the maximum in the magnetic susceptibility at the Fermi surface nesting vector Q_N. The phase diagram for the magnetic structures is presented, however several properties of the Q_N magnetic structure cannot be explained within any known models. Quadrupolar ordering is suggested as a possible candidate for explaining these features of the Q_N structure. (au)