High damping materials exhibiting a loss factor higher than 10-2 are generally considered as polymer or metallic materials. But, it will be interesting to consider ferroelectric or ferrimagnetic ceramics, in which internal friction can be due to the motion of ferroelectric or magnetic domains. High level of internal friction can be obtained in these ceramics in a given temperature range. In the case of ferroelectric ceramics, hard ferroelectrics, such as BaTiO3 or PZT, can show some relaxation peaks below the Curie temperature due the motion of domain walls and the interaction between the domain walls and the oxygen vacancies or cationic vacancies. In the case of ferrimagnetic ceramics, some anelastic manifestations due to the ferrimagnetic domain walls appear below the Curie Temperature TC. These peaks are linked to the interaction of domain walls with cation vacancies or cation interstitials or the lattice. Above the Curie temperature, a relaxation mechanism due to the exchange of cations Mn3+ and their vacancies on octahedral sites should occur.