Using an approach in line with that of a previous report, we assessed the antioxidant activity of several natural, polyphenol- or tocotrienol-rich mixtures: extracts from Elaesis Guineensis oil (A) and Vitis vinifera (B), a Coffea robusta powder (C), and extracts from Olea europea mill wastewaters (D), Solanum melongena (E), and Lycopersicon esculentum (F). The copper- and 2-2'-azobis(2-amidinopropane) hydrochloride (AAPH)-oxidation systems were used in the presence of low-density lipoprotein. For comparison, antioxidant activities of chlorogenic acid and catechin, as archetypes of molecules highly efficient with the copper- and the AAPH-oxidation system, respectively, were assessed. The aim was to establish the occurrence of synergistic antioxidant actions among some of these natural mixtures. On a molar basis, the highest specific antioxidant activities (SAA) were found for B, chlorogenic acid, and C in the copper system, and for A, catechin, and B in the AAPH system. On a mass basis, the highest SAA were found, respectively, for chlorogenic acid, B, and catechin, and for catechin, chlorogenic acid, and B. These results show that large discrepancies take place in the evaluations between the two systems. B and C exhibited a synergistic antioxidant efficiency, in the presence or absence of A, but only with the copper system. This was also true for the two types of A+B+C mixture that were tested. It is thought that this association might provide an ideal combination, incorporating both the radical scavenger and the transition-metal ion chelation properties of B and C.