The dependence of humans on oxygen for their metabolism, together with their uninterrupted exposure to a wide variety of hazardous environmental chemicals, leads to the continuous formation of reactive oxygen-derived species (ROS) in the body, such as superoxide radical anion, hydrogen peroxide, peroxyl radicals, and hydroxyl radical. When in excess, ROS can damage cellular constituents such as DNA and membrane lipids causing oxidative stress, cellular injury, and, eventually, inflammatory, neoplastic, diabetic, cardiovascular, neurodegenerative, and age-related diseases. Fortunately, the body has a multitude of naturally occurring antioxidants in dietary fruits and vegetables to its disposal, including polyphenolic compounds, vitamins, and essential minerals. These antioxidants eliminate ROS by acting as reducing agents, hydrogen donors, quenchers of singlet oxygen, or chelators of metal ions that catalyze oxidation reactions, thus decreasing the risk of the abovementioned diseases. This first part of the current chapter comprehensively addresses three representative examples of fruits from the Republic of Suriname (South America) that are rich in anthocyanins, ellagitannins, and coumarins and highlights their antioxidant activity and beneficial and health-promoting effects. In part 2, four Surinamese fruits with an abundance of (pro)vitamins A, C, and E and selenium are equally extensively dealt with in light of their antioxidant activities.