Dimethyl terephthalate is prepared by the continuous esterification of terephthalic acid in the gas phase by evaporating solid terephthalic acid in a pre-reactor by means of a hot methanol vapor stream, conducting the gas mixture through a solid bed catalyst in a follow-up reactor, and recirculating a portion of the reaction product to the pre-reactor. After the pre-reactor the terephthalic acid dispersed in the methanol gas phase is heated and vaporized in one or more consecutive heat exchangers followed by one or more dwell period lengths and immediately heated to the esterification temperature prior to entry into the follow-up reactor.