Recently, it has been shown that a new class of quasi-one-dimensional conductors can be created by doping discotic liquid crystals with appropriate oxidants. This paper reports the elucidation of the mechanism of conduction in these new materials. In particular, the ac conductivity of 2,3,6,7,10,11-hexahexyloxytriphenylene (HAT6) doped with the Lewis acid AlCl3, has been measured as a function of frequency (10−3–107 Hz), and temperature in its crystalline solid (K), hexagonal discotic liquid crystal (Dho), and isotropic liquid (I) phases. In all three phases the conductivity is independent of frequency at low frequencies, but shows a power law dependence on frequency [σ(ω)∼ωs, s∼0.7–0.8] at higher frequencies. This behavior is characteristic of charge carrier transport by a hopping mechanism. The conductivity data have been analyzed in terms of the Scher and Lax theory to obtain the parameters describing this process. In macroscopically aligned K and Dho phases, the conductivity measured along the column axes is approximately 103 greater than that in the perpendicular direction. The conduction along the columns is identified with a single charge transport process in which the carriers hop between localized states (radical cations) associated with AlCl4−-counterions linearly distributed off-axis along the columns. The charge carrier diffusion coefficient is independent of the concentration of dopant and has the value D∥∼3.4×10−10 m2 s−1 in the Dho phase at 343 K. In the isotropic melt phase, the conductivity measurements reveal the involvement of two distinct processes. One of these is identified with charge migration along supramolecular ‘‘stacks’’ some 200 nm in length, whilst the other appears to be associated with carriers hopping between these stacks. The conductivity behavior of the unaligned Dho and K phases is very similar to that of the isotropic liquid phase implying that the mesoscopic structure of the latter phase is ‘‘frozen-in’’ as a ‘‘defect structure’’ on cooling. This defect structure then dominates the conductivity behavior of the unaligned Dho and K phases.