Down Syndrome (DS), or trisomy 21, occurs in one out of 700-1000 live births. It is commonly observed that DS patients present obesity and zinc deficiency. Zinc deficiency could be related to overactivity of the enzyme Cu/Zn Superoxide Dismutase (SOD) in these individuals. As a result of this overactivity, individuals with DS are in a state of continuous Oxidative Stress (OS). The aim of this study was to evaluate the nutritional status of individuals with DS, and to measure dietary zinc intake and blood zinc levels, as well OS markers, especially SOD. There were twenty-five children in the DS group aged between 2 and 19. In the control group, there were thirty-two individuals with the same age profile. There was an increased percentage of obesity and overweight in the DS group patients. There was no inadequate consumption or blood zinc deficiency in either group. We observed a reduction in the antioxidant enzymes SOD and Catalase (CAT) in the DS group as well as an increase in thiobarbituric acid-reactive substances (TBARS). This suggests a state of OS in the DS group. Unlike other studies, this study found no zinc deficiency or SOD overactivity in individuals with DS compared to the control group. There was OS in these patients as evidenced by higher levels of TBARS. However, unexpectedly, this elevation was related to a reduction of SOD and CAT activity. It is suggested that more studies should be conducted in this area to clarify the issue.