One exemplary embodiment can be a process for the isomerization of a non-equilibrium alkylaromatic feed mixture. The process can include contacting the non-equilibrium alkylaromatic feed mixture in a C8 isomerization zone. The C8 isomerization zone may include a first isomerization stage and a second isomerization stage. At the first isomerization stage, at least a portion of the non-equilibrium alkylaromatic feed mixture can be contacted at a first isomerization condition in a liquid phase in the substantial absence of hydrogen to obtain an intermediate stream. At the second isomerization stage, at least part of the intermediate stream and at least a part of a stream rich in at least one naphthene can be contacted at a second isomerization condition to obtain a concentration of at least one alkylaromatic isomer that is higher than a concentration of that at least one alkylaromatic isomer in the non-equilibrium alkylaromatic feed mixture.