A number of hypotheses have been advanced to explain the rapid increase of the incidence of esophageal adenocarcinoma in the US. A major problem in identifying and understanding the nature of this increase is the difficulty in untangling age effects from temporal trends due to cohort and period effects. To address this problem, we have developed multi-stage carcinogenesis models that describe the age-specific incidence of adenocarcinoma of the esophagus and of the gastric cardia with separate adjustments for temporal trends. These models explicitly incorporate important features of the cancers, such as the metaplastic conversion of normal esophagus to Barrett's esophagus (BE). We fit these models separately to the incidence of adenocarcinoma of the esophagus and of the gastric cardia reported in the Surveillance Epidemiology and End Results (SEER) registry over the period 1973-2000. We conclude that the incidence of both cancers is consistent with a sequence that posits a tissue conversion step in the target organ followed by a multi-stage process with three rate-limiting events, the first two leading to an initiated cell that can expand clonally into a premalignant lesion, and the third converting an initiated cell into a malignant cell. Temporal trends in the incidence of both cancers are dominated by dramatically increasing period effects.