Flavonoids, secondary plant metabolites with many health-promoting properties, including antioxidant, are a valuable component of food products, especially functional foods. In the latter, plant extracts are commonly used, the properties of which are attributed to the characteristic main ingredients. However, in a mixture the antioxidant properties of the individual ingredients do not always show an additive effect. This paper presents and discusses the antioxidant properties of naturally occurring flavonoid aglycones and their binary mixtures. In the experiments, model systems were used that differed in the volume of the alcoholic antioxidant solution in the measuring system and its concentration in the range in which it occurs in nature. Antioxidant properties were determined by ABTS and DPPH methods. The presented data proved that the dominant resultant effect in the mixtures is antioxidant antagonism. The magnitude of the observed antagonism depends on the mutual relations of individual components, their concentrations and the method used to assess antioxidant properties. It was shown that the observed non-additive antioxidant effect of the mixture results from the formation of intramolecular hydrogen bonds between phenolic groups of the antioxidant molecule. The presented results may be useful in the context of proper design of functional foods.