Amyotrophic lateral sclerosis (ALS) and frontotemporal dementia (FTD) are fatal neurodegenerative diseases characterized by the presence of neuropathological aggregates of phosphorylated TDP-43 (P-TDP-43) protein. The RNA-binding protein TDP-43 participates also to cell stress response by forming stress granules (SG) in the cytoplasm to temporarily arrest translation. The hypothesis that TDP-43 pathology directly arises from SG has been proposed but is still under debate because only sub-lethal stress conditions have been tested experimentally so far. In this study we reproduced a mild and chronic oxidative stress by sodium arsenite to better mimic the persistent and subtle alterations occurring during the neurodegenerative process in primary fibroblasts and induced pluripotent stem cell-derived motoneurons (iPSC-MN) from ALS patients carrying mutations in TARDBP and C9ORF72 genes. We found that not only the acute sub-lethal stress usually used in literature, but also the chronic oxidative insult was able to induce SG formation in both primary fibroblasts and iPSC-MN. We also observed the recruitment of TDP-43 into SG only upon chronic stress in association to the formation of distinct cytoplasmic P-TDP-43 aggregates and a significant increase of the autophagy marker p62. A quantitative analysis revealed differences in both the number of cells forming SG in mutant ALS and healthy control fibroblasts, suggesting a specific genetic contribution to cell stress response, and in SG size, suggesting a different composition of these cytoplasmic foci in the two stress conditions. Upon removal of arsenite, the recovery from chronic stress was complete for SG and P-TDP-43 aggregates at 72 h with the exception of p62, which was reduced but still persistent, supporting the hypothesis that autophagy impairment may drive pathological TDP-43 aggregates formation. The gene-specific differences observed in fibroblasts in response to oxidative stress were not present in iPSC-MN, which showed a similar formation of SG and P-TDP-43 aggregates regardless their genotype. Our results show that SG and P-TDP-43 aggregates may be recapitulated in patient-derived neuronal and non-neuronal cells exposed to prolonged oxidative stress, which may be therefore exploited to study TDP-43 pathology and to develop individualized therapeutic strategies for ALS/FTD.