In a process for separating dimethyl biphenyl isomers a mixture comprising one or more 3,3′, 3,4′- or 4,4′-dimethyl biphenyl isomers, one or more 2,X′-dimethyl biphenyl isomers (where X=2, 3, or 4) and one or more further hydrocarbon components is contacted with a first adsorbent, thereby selectively adsorbing one or more of the dimethyl biphenyl isomers within the first adsorbent. A first raffinate stream containing less selectively adsorbed components is withdrawn from the first adsorbent and a first extract stream containing selectively adsorbed dimethyl biphenyl isomers is withdraw. The selectively adsorbed dimethyl biphenyl isomers comprise one or more of 3,3′-, 3,4′- or 4,4′-dimethyl biphenyl isomers and one or more of 2,X′-dimethyl biphenyl isomers (where X′=2, 3, or 4).