RCu 2 ͑R = rare earth͒ is presented as the first magnetic shape memory ͑MSM͒ alloy with the magnetic anisotropy of rare earth ions as impelling force. Besides La 2−x Sr x CuO 4 RCu 2 is the second known antiferromagnetic MSM-compound system. However, longrange magnetic order is not necessary for the MSM effect here. Microstructural changes are occurring even above the magnetic ordering temperature because the magnetic anisotropy gives a strong effect also in the paramagnetic state. RCu 2 compounds have a pseudohexagonal orthorhombic structure which splits up into three twin variants, each rotated about 60°to the others about the pseudohexagonal axis. To move the twin boundaries, a magnetic field of about 3.2 T and a temperature of typical 30 K is necessary. Moving of twin boundaries results in a typical length change of two percent. Depending on the field direction a certain twin variant is favored. Neutron data from a Tb 0.5 Dy 0.5 Cu 2 single crystal confirm a change of the volume fraction of the three twin variants.