The chemical constituents of the hexane and methanol extracts obtained from the branch bark of Bursera simaruba (Burseraceae) grown in Queretaro, Mexico, were investigated by GC-MS, HPLC coupled to DAD, and NMR techniques. Seventeen compounds, including terpenoids, flavonoids, phenolic acids, long-chain fatty acids (FA), methyl esters of FA and sucrose, were identified. In addition, an assessment of the antiradical activity of the methanol extract (ME) was also carried out using DPPH, ABTS, FRAP and DPV assays. The DPPH, ABTS and FRAP assays showed a low antioxidant capacity for the ME. This was in accordance with the relatively low quantities of phenols found in the extract. However, according to the differential pulse voltammetry assay (DVP), this extract exhibited an oxidation potential close to those of quercetin and (+)-catechin, two of the flavonoids with recognized good antioxidant power. This indicated that the ME does contain compounds with good antioxidant capacity and suggested that sometimes the most popular methods commonly used might be underestimating the true antioxidant capacities of plant samples and how the DPV is a valuable complementary tool to be taken into consideration when conducting these in vitro assays.