The dielectric and ac/dc transport properties of single crystals of yttrium iron garnet (Y3Fe5O12 and Y3Fe5O12:Si), and barium hexaferrite (BaFe12O19 and BaFe12O1 9:Co,Ti) were investigated after irradiations with Xe and Pb ions in the GeV range. In the virgin n-type samples (Y3Fe5O12:Si and BaFe12O19:Co,Ti), the strong dielectric relaxation below 100 kHz is found to correspond to a space-charge polarization at the blocking metal/insulator contacts yielding a nonohmic dc conductivity. The relaxation frequency decreases with increasing amorphization yield in relation to the decrease of the insulators bulk dc conductivity which becomes ohmic in the amorphous phases. The ac conductivity data of both crystalline and amorphous Y3Fe5O12:Si above 100 kHz and for 100 K≪T≪300 K exhibit two contributions: (i) that of carrier transport in a disordered or inhomogeneous medium varying as νs, with s≃0- .8, (ii) and that of a two-site polaron hopping process of charge transfer between Fe2+ and Fe3+ with an activation energy of 0.29 eV for T≫180 K. The dc conductivity data of crystalline Y3Fe5O12:Si for 80 K≪T≪300 K are discussed on the basis of a small polaron hopping conduction mechanism between Fe2+ and Fe3+ with an activation energy around 0.28 eV for T≫125 K, in agreement with the activation energy around 0.28 eV of the space-charge dielectric relaxation frequency for T≫180 K. All amorphous phases data are consistent with the picture of hopping conduction between gap states in a disordered medium with (i) an νs dependence for the ac conductivity above a critical frequency proportional to the dc conductivity, (ii) and an exp(-T-1/4) law for the dc conductivity. © 1997 American Institute of Physics.