The oxidative potential (OP) of particulate matter (PM) measures PM capability to potentially cause anti-oxidant imbalance. Due to the wide range and complex mixture of species in particulates, little is known about the pollution sources most strongly contributing to OP. A 1-year sampling of PM.sub.10 (particles with an aerodynamic diameter below 10) was performed over different sites in a medium-sized city (Grenoble, France). An enhanced fine-scale apportionment of PM.sub.10 sources, based on the chemical composition, was performed using the positive matrix factorization (PMF) method and reported in a companion paper (Borlaza et al., 2020). OP was assessed as the ability of PM.sub.10 to generate reactive oxygen species (ROS) using three different acellular assays: dithiothreitol (DTT), ascorbic acid (AA), and 2,7-dichlorofluorescein (DCFH) assays. Using multiple linear regression (MLR), the OP contributions of the sources identified by PMF were estimated. Conversely, since atmospheric processes are usually non-linear in nature, artificial neural network (ANN) techniques, which employ non-linear models, could further improve estimates. Hence, the multilayer perceptron analysis (MLP), an ANN-based model, was additionally used to model OP based on PMF-resolved sources as well. This study presents the spatiotemporal variabilities of OP activity with influences by season-specific sources, site typology and specific local features, and assay sensitivity. Overall, both MLR and MLP effectively captured the evolution of OP. The primary traffic and biomass burning sources were the strongest drivers of OP in the Grenoble basin. There is also a clear redistribution of source-specific impacts when using OP instead of mass concentration, underlining the importance of PM redox activity for the identification of potential sources of PM toxicity. Finally, the MLP generally offered improvements in OP prediction, especially for sites where synergistic and/or antagonistic effects between sources are prominent, supporting the value of using ANN-based models to account for the non-linear dynamics behind the atmospheric processes affecting OP of PM.sub.10.