Degradation of unwanted proteins is important in protein quality control cooperating with the dynein/dynactin-mediated trafficking along the acetylated microtubule (MT) network. Proteins associated directly/indirectly with tubulin/MTs play crucial roles in both physiological and pathological processes. Our studies focus on the interrelationship of the tubulin deacetylase HDAC6, the MT-associated TPPP/p25 with its deacetylase inhibitory potency and the hub dynein light chain DYNLL/LC8, constituent of dynein and numerous other protein complexes. In this paper, evidence is provided for the direct interaction of DYNLL/LC8 with TPPP/p25 and HDAC6 and their assembly into binary/ternary complexes with functional potency. The in vitro binding data was obtained with recombinant proteins and used for mathematical modelling. These data and visualization of their localizations by bimolecular fluorescence complementation technology and immunofluorescence microscopy in HeLa cells revealed the promoting effect of TPPP/p25 on the interaction of DYNLL/LC8 with both tubulin and HDAC6. Localization of the LC8-2-TPPP/p25 complex was observed on the MT network in contrast to the LC8-2-HDAC6 complex, which was partly translocated to the nucleus. LC8-2 did not influence directly the acetylation of the MT network. However, the binding of TPPP/p25 to a new binding site of DYNLL/LC8, outside the canonical binding groove, counteracted the TPPP/p25-derived hyperacetylation of the MT network. Our data suggest that multiple associations of the regulatory proteins of the MT network could ensure fine tuning in the regulation of the intracellular trafficking process either by the complexation of DYNLL/LC8 with new partners or indirectly by the modulation of the acetylation level of the MT network.