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 ofsuperconductivity. 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 , the minority domain (QNB = (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 graduallysuppressed 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 , the magnetic structure rotates a small angle of 0.5 degrees away from the symmetrydirection. TmNi2B2C: A magnetic field applied in the  direction suppresses the zero field magnetic structure QF = (0.094,0.094,0) (TN = 1.6 K), in favor of the Fermi surface nesting structure QN = (0.483,0,0). The appearance of the QN phase wasinitially 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 QN.The phase diagram for the magnetic structures is presented, however several properties of the QN magnetic structure cannot be explained within any known models. Quadrupolar ordering is suggested as a possible candidate for explaining these features ofthe QN structure.