BACKGROUND: WHO guidelines recommend dolutegravir plus two nucleoside reverse transcriptase inhibitors (NRTIs) for second-line HIV therapy, with NRTI switching from first-line tenofovir to zidovudine. We aimed to examine whether dolutegravir is non-inferior to darunavir, the best-in-class protease inhibitor drug, and whether maintaining tenofovir in second-line therapy is non-inferior to switching to zidovudine. METHODS: In this prospective, multicentre, open-label, factorial, randomised, non-inferiority trial (NADIA), participants with confirmed HIV first-line treatment failure (HIV-1 RNA ≥1000 copies per mL) were recruited at seven clinical sites in Kenya, Uganda, and Zimbabwe. Following a 2 × 2 factorial design and stratified by site and screening HIV-1 RNA concentration, participants were randomly assigned (1:1:1:1) to receive a 96-week regimen containing either dolutegravir (50 mg once daily) or ritonavir-boosted darunavir (800 mg of darunavir plus 100 mg of ritonavir once daily) in combination with either tenofovir (300 mg once daily) plus lamivudine (300 mg once daily) or zidovudine (300 mg twice daily) plus lamivudine (150 mg twice daily). The NRTI drugs allocated by randomisation were administered orally in fixed-dose combination pills; other drugs were administered orally as separate pills. The previously reported primary outcome was the proportion of participants with a plasma HIV-1 RNA concentration of less than 400 copies per mL at 48 weeks. Here, we report the main secondary outcome: the proportion of participants with a plasma HIV-1 RNA concentration of less than 400 copies per mL at 96 weeks (non-inferiority margin 12%). We analysed this outcome and safety outcomes in the intention-to-treat population, which excluded only those who were randomly assigned in error and withdrawn before receiving trial drugs. This study was registered at ClinicalTrials.gov, NCT03988452, and is complete. FINDINGS: Between July 30 and Dec 18, 2019, we screened 783 patients and enrolled 465. One participant was randomly assigned in error and immediately withdrawn. The remaining 464 participants were randomly assigned to receive either dolutegravir (n=235) or ritonavir-boosted darunavir (n=229) and to receive lamivudine plus either tenofovir (n=233) or zidovudine (n=231). At week 96, 211 (90%) of 235 participants in the dolutegravir group and 199 (87%) of 229 participants in the darunavir group had HIV-1 RNA less than 400 copies per mL (percentage point difference 2·9, 95% CI -3·0 to 8·7), indicating non-inferiority. Nine (4%) participants (all in the dolutegravir group) developed dolutegravir resistance; no participants developed darunavir resistance (p=0·0023). In the other randomised comparison, 214 (92%) of 233 patients in the tenofovir group and 196 (85%) of 231 patients in the zidovudine group had HIV-1 RNA less than 400 copies per mL (percentage point difference 7·0, 95% CI 1·2 to 12·8), showing non-inferiority and indicating the superiority of tenofovir (p=0·019). The proportions of participants with any grade 3-4 adverse event were similar between the dolutegravir (26 [11%]) and darunavir (28 [12%]) groups and between the tenofovir (22 [9%]) and zidovudine (32 [14%]) groups. There were no deaths related to study medication. INTERPRETATION: Dolutegravir-based and darunavir-based regimens maintain good viral suppression during 96 weeks; dolutegravir is non-inferior to darunavir but is at greater risk of resistance in second-line therapy. Tenofovir should be continued in second-line therapy, rather than being switched to zidovudine. FUNDING: Janssen.