Epidemiological surveys have shown an inverse relationship between the intake of fruit and the incidence of coronary heart disease and some type of cancer. Data found in the literature regarding the flavonoids in general while this study focuses on flavanones, a subclass of flavonoids which occurs in Citrus fruit. The aim of this work is to elucidate the antioxidant or pro-oxidant behaviours of some common flavanones and to determine their activity–structure relationships as antioxidant using the crocin bleaching inhibition assay. The compounds studied were regarding both the aglycon form and the glycoside form. Data evidence that the substitution of the 7th OH group of the flavanones by a neohesperidoside influences the relationship between structure and antioxidant activity. In fact, the 3′,4′-catechol structure and the O-methylation, in the aglycone forms, do not result significant. On the other hands, in the glycosylate forms, the 3′,4′-catechol structure noticeably increases the antioxidant power and the O-methylation decreases the antioxidant activity. The influence of the O-glycosylation with a rutinose molecule is neglectable.