We have made extensive studies of the charge-carrier mobilities in the discotic hexagonal mesophases of triphenylene-based discotic liquid crystals. Using the time-of-flight technique, transient photocurrents were measured yielding charge-carrier mobilities for various electric fields and temperatures. Starting from promising results obtained with the monomeric discotic liquid crystalline model compound hexapentyloxytriphenylene (H5T), we synthesized a "discotic twin" with two triphenylene units linked together by a suitable spacer. Additionally, we synthesized a discotic liquid crystalline oligomer consisting of four triphenylene units which are bound to a flexible cyclosiloxane ring. In the dimer and in the oligomer the discotic mesophase can be maintained in a discotic glass. Our data show that in both H5T as well as in the dimer and in the oligomer hole mobilities on the order of magnitude of 10(-3)cm(2)/Vs can be reached. Since the mobilities obtained in the oligomeric compounds are comparable to those found in the monomeric model compound, it becomes clear that the excellent charge-carrier transport properties in the discotic hexagonal mesophase can be preserved in easily processible and anisotropic organic thin films. Therefore, our results are an important step towards the applicability of highly ordered discotic liquid crystalline materials in the field of electronic applications.