Materials with a large capacity to dissipate mechanical energy are of interest for passive vibration damping. We have measured the zero-field damping capacity of the giant magnetostrictive terbium-dysprosium-iron compounds by quasistatic stress-strain hysteresis loops. The magnetization and strain of the samples were measured for increasing and decreasing compressive stresses, up to 50 MPa. The zero-field, room temperature damping capacity (Delta W/W) was calculated from the stressstrain loops and is plotted against maximum stress. The damping capacity maximum for the alloy with the nominal Terfenol-D composition occurs at 4.1 MPa with the value 1.75 which corresponds to Q(-1)=0.28. The damping is almost independent of stress in a multi-phase sample, (Tb0.6Dy0.4)Fe-1.4, which contains both Laves phase and elemental rare earth. (C) 1996 American Institute of Physics.