The shape-selective transalkylation of biphenyl with pentamethylbenzene over ultrastable Y-faujasites to produce para-methylated biphenyls was studied in the liquid slurry phase. The reaction was carried out in a discontinuously operated stainless steel autoclave using n-heptane as the solvent with a temperature range of 513 to 533 K and a pressure of 3 MPa. As for the progress of the reaction the presence of strong Bronsted acid sites was essential, an ultrastable faujasite treated with aqueous hydrochloric acid having a high content of those sites was used as the catalyst. Thus, a yield of the target product 4,4＇-dimethylbiphenyl of above 11% referring to biphenyl could be achieved. The effect of the operating conditions on the formation of the target product was investigated. The decisive influence was acted out by the molar ratio of biphenyl to alkylating agent, in so far as a surplus of pentamethylbenzene of 7:1 referring to biphenyl enhanced the yield of the target product to 14%. The kinetics of the reaction could be successfully described with a lumped reaction scheme, introducing pseudo components, summarizing structural isomers, and pseudo reactions, such as the formation of coke.