A process is described for producing paraxylene, in which an aromatic hydrocarbon feedstock comprising benzene and/or toluene is contacted with an alkylating reagent comprising methanol and/or dimethyl ether in an alkylation reaction zone under alkylation conditions in the presence of an alkylation catalyst to produce an alkylated aromatic product comprising xylenes. The alkylation catalyst comprises a molecular sieve having a Constraint Index≤5, and the alkylation conditions comprise a temperature less than 500° C. Paraxylene may then be recovered from the alkylated aromatic product.