  We present a thorough dielectric investigation of the hexagonal perovskites
La1.2Sr2.7IrO7.33 and La1.2Sr2.7RuO7.33 in a broad frequency and temperature
range, supplemented by additional infrared measurements. The occurrence of
giant dielectric constants up to 10^5 is revealed to be due to electrode
polarization. Aside of dc and ac conductivity contributions, we detect two
intrinsic relaxation processes that can be ascribed to ionic hopping between
different off-center positions. In both materials we find evidence for charge
transport via hopping of localized charge carriers. In the infrared region,
three phonon bands are detected, followed by several electronic excitations. In
addition, these materials provide further examples for the occurrence of a
superlinear power law in the broadband ac conductivity, which recently was
proposed to be a universal feature of all disordered matter.
