For patients with advanced non-small-cell lung cancer (NSCLC), dual immune checkpoint blockade (ICB) with CTLA4 inhibitors and PD-1 or PD-L1 inhibitors (hereafter, PD-(L)1 inhibitors) is associated with higher rates of anti-tumour activity and immune-related toxicities, when compared with treatment with PD-(L)1 inhibitors alone. However, there are currently no validated biomarkers to identify which patients will benefit from dual ICB1,2. Here we show that patients with NSCLC who have mutations in the STK11 and/or KEAP1 tumour suppressor genes derived clinical benefit from dual ICB with the PD-L1 inhibitor durvalumab and the CTLA4 inhibitor tremelimumab, but not from durvalumab alone, when added to chemotherapy in the randomized phase III POSEIDON trial3. Unbiased genetic screens identified loss of both of these tumour suppressor genes as independent drivers of resistance to PD-(L)1 inhibition, and showed that loss of Keap1 was the strongest genomic predictor of dual ICB efficacy-a finding that was confirmed in several mouse models of Kras-driven NSCLC. In both mouse models and patients, KEAP1 and STK11 alterations were associated with an adverse tumour microenvironment, which was characterized by a preponderance of suppressive myeloid cells and the depletion of CD8+ cytotoxic T cells, but relative sparing of CD4+ effector subsets. Dual ICB potently engaged CD4+ effector cells and reprogrammed the tumour myeloid cell compartment towards inducible nitric oxide synthase (iNOS)-expressing tumoricidal phenotypes that-together with CD4+ and CD8+ T cells-contributed to anti-tumour efficacy. These data support the use of chemo-immunotherapy with dual ICB to mitigate resistance to PD-(L)1 inhibition in patients with NSCLC who have STK11 and/or KEAP1 alterations.