In a process for producing one or more 2,X′-dimethyl biphenyl isomers (where X=2, 3 or 4), a feed comprising toluene is contacted with hydrogen in the presence of a hydroalkylation catalyst under conditions effective to produce a hydroalkylation reaction product comprising (methylcyclohexyl)toluene. At least part of the hydroalkylation reaction product is dehydrogenated in the presence of a dehydrogenation catalyst under conditions effective to produce a dehydrogenation reaction product comprising dimethyl biphenyl isomers. The dehydrogenation reaction product is then separated into at least a first stream comprising one or more 3,3′-, 3,4′- and 4,4′-dimethyl biphenyl isomers and at least one second stream comprising one or more 2,X′-dimethyl biphenyl isomers (where X=2, 3 or 4). The at least one second stream is then contacted with a first adsorbent thereby selectively adsorbing one or more 2,X′-dimethyl biphenyl isomers (where X=2, 3 or 4) within said first adsorbent and then withdrawing from said first adsorbent a first extract stream comprising one or more selectively adsorbed 2,X′-dimethyl biphenyl isomers (where X=2, 3 or 4) and a first raffinate stream comprising one or more less selectively adsorbed components.