SummaryHomeostasis of postmitotic and proliferating cells is maintained by pathways that repress stress. We found that the Caenorhabditis elegans histone 3 lysine 4 (H3K4) demethylases RBR‐2 and SPR‐5 promoted postmitotic longevity of stress‐resistant daf‐2 adults, altered pools of methylated H3K4, and promoted silencing of some daf‐2 target genes. In addition, RBR‐2 and SPR‐5 were required for germ cell immortality at a high temperature. Transgenerational proliferative aging was enhanced for spr‐5; rbr‐2 double mutants, suggesting that these histone demethylases may function sequentially to promote germ cell immortality by targeting distinct H3K4 methyl marks. RBR‐2 did not play a comparable role in the maintenance of quiescent germ cells in dauer larvae, implying that it represses stress that occurs as a consequence of germ cell proliferation, rather than stress that accumulates in nondividing cells. We propose that H3K4 demethylase activities promote the maintenance of chromatin states during stressful growth conditions, thereby repressing postmitotic aging of somatic cells as well as proliferative aging of germ cells.