In this study the proper maintenance dose of oral Omeprazole will be determined in each patient by determining the minimal dose of drug that reduces acid secretion to safe levels. Patients will be examined at least annually for evidence of continued efficacy and safety. Efficacy will be assessed by clinical history to assess control of symptoms due to gastric acid hypersecretion, measurements of gastric acid secretion while on Omeprazole to determine continued effectiveness of the drug and upper gastrointestinal endoscopy to assess changes in the gastrointestinal mucosa. Safety will be determined by assessing clinical and laboratory parameters such as changes in hematologic or clinical chemistry parameters. Possible drug induced changes in the gastric mucosa will be assessed by gastric biopsies.