A process for the tertiary dealkylation of a tertiary alkyl containing m- and/or p-cresol wherein a tertiary alkyl containing m- and/or p-cresol is continously introduced into a reaction vessel with a small amount of sulfuric acid or an quivalent amount of a sulfonic acid and the reaction vessel contains a high concentration of m- and/or p-cresol or a high boiling phenol which under the prevailing reaction conditions is not substantially vaporized from the reaction mixture. The reaction mixture is maintained at a temperature of no greater than 230.degree. C. The reaction products are withdrawn continuously from the reactor (and separated into its components) and at the same time a small amount of the reaction mixture being withdrawn intermittently or continously from the reactor.