The well-known antioxidant activity of red wine is explained mostly by its polyphenols content, where the final effect is based on the wine components' interaction. The aim of our work was the study of the interaction of three red wine polyphenols--quercetin, resveratrol and caffeic acid--alone and in their equimolar binary and ternary mixtures in different antioxidant/scavenging assays (inhibition of 2-deoxy-D-ribose degradation by hydroxyl radical, FRAP, Fe(III) reducing power, DPPH, ABTS and NO scavenging, respectively). Interaction analysis, based on median effect equation, was performed for the determination of synergy and/or antagonism. The obtained results indicate that the mutual interactions of tested polyphenols in their mixtures are markedly different from each other, depending on the reaction mechanism of the assay used. The measured antioxidant activity of individual polyphenols is not a constant value when other substances are present in the mixture with this polyphenol. Interactions can cause the finally observed synergy/antagonism/additive effects without any possibility of predicting them from the known activities of single compounds. This “unpredictability” claim based on in vitro assay results should be very important in multiple systems and processes in Nature, where the interactions among compounds in mixtures need to be take into account.