The phase behavior of two unsymmetrical triphenylene crown ether-based columnar liquid crystals bearing different lengths of alkyl chains, KAL465 and KAL468, was investigated using differential scanning calorimetry (DSC). A plastic crystalline (Cry), a columnar liquid crystalline (Col(h)), and an isotropic phase were observed along with two glass transitions in the Cry phase. The molecular mobility of the KAL compounds was further studied by a combination of broadband dielectric spectroscopy (BDS) and advanced calorimetric techniques. By the BDS investigations, three dielectric active relaxation processes were observed for both samples. At low temperatures, a gamma-process in the Cry state was detected and is assigned to the localized fluctuations taking place in the alkyl chains. An alpha(2)-process takes place at higher temperatures in the Cry phase. An alpha(3)-process was found in the Col(h) mesophase. The advanced calorimetric techniques consist of fast scanning calorimetry (FSC) and specific heat spectroscopy employing temperature-modulated DSC and FSC. The advanced calorimetric investigations revealed that besides the alpha(2)-process in agreement with BDS, there is a second dynamic glass transition (alpha(1)-process), which is not observed by dielectric spectroscopy. The results are in good agreement with the glass transitions detected by DSC for this process. The temperature dependences of the relaxation rates of the alpha(1)-, alpha(2)-, and alpha(3)-processes are all different. Therefore, different molecular assignments for the relaxation processes are proposed. In addition to the relaxation processes, a conductivity contribution was explored by BDS for both KAL compounds. The conductivity contribution appears in both Cry and Col(h) phases, where the conductivity increases by ca. 1 order of magnitude at phase transition from the Cry to the hexagonal phase.