Using a combination of solid state2H NMR spectroscopy on selectively deuteriated samples and dielectric spectroscopy, the molecular dynamics of discotic charge-transfer (CT) complexes were investigated. These complexes show particular thermodynamic and flow properties. Considered were mixtures of low molar mass donors and acceptors, low molar mass donors with main chain acceptor polymers and covalently linked donor-acceptor twins with different lengths of the spacer. A main result is that correlated rotational motions of discotic molecules or groups about the columnar axis are observed in all systems except for the twin with the short spacer. This type of motion seems to be a general feature of columnar phases. The non-discotic acceptor which is incorporated in the columns participates in this motion. The twin possessing a long spacer displays at high temperatures an additional process: it performs a diffusion process between the columns. A further result is that broad biphasic regions exist in CT mixtures at the transition from the discotic to the isotropic state.