High damping alloys based on Mn and Fe with different damping mechanisms are discussed. In Mn-Cu alloys the nature of damping depends on concentration. At lower Cu concentration it comes from the specific twinned fcc-fct structure with very high density and mobility of the twin boundaries. Forca. 60% Cu alloys it is caused by reorientation of the axes of the fct precipitates in the fcc matrix. In Fe-Cr alloys high damping results from a magnetomechanical mechanism. Applications of the described high damping alloys are also reviewed.