Summary Background Concomitant chemoradiotherapy and accelerated radiotherapy independently improve outcomes for patients with locally advanced head and neck squamous-cell carcinoma (HNSCC). We aimed to assess the efficacy and safety of a combination of these approaches. Methods In our open-label phase 3 randomised trial, we enrolled patients with locally advanced, stage III and IV (non-metastatic) HNSCC and an Eastern Cooperative Oncology Group performance status of 0–2. We randomly allocated patients centrally with a computer program (with centre, T stage, N stage, and localisation as minimisation factors) in a 1:1:1 ratio to receive conventional chemoradiotherapy (70 Gy in 7 weeks plus three cycles of 4 days' concomitant carboplatin-fluorouracil), accelerated radiotherapy-chemotherapy (70 Gy in 6 weeks plus two cycles of 5 days' concomitant carboplatin-fluorouracil), or very accelerated radiotherapy alone (64·8 Gy 1·8 Gy twice daily in 3·5 weeks). The primary endpoint, progression-free survival (PFS), was assessed in all enrolled patients. This trial is completed. The trial is registered with ClinicalTrials.gov , number NCT00828386. Findings Between Feb 29, 2000, and May 9, 2007, we randomly allocated 279 patients to receive conventional chemoradiotherapy, 280 to accelerated radiotherapy-chemotherapy, and 281 to very accelerated radiotherapy. Median follow-up was 5·2 years (IQR 4·9–6·2); rates of chemotherapy and radiotherapy compliance were good in all groups. Accelerated radiotherapy-chemotherapy offered no PFS benefit compared with conventional chemoradiotherapy (HR 1·02, 95% CI 0·84–1·23; p=0·88) or very accelerated radiotherapy (0·83, 0·69–1·01; p=0·060); conventional chemoradiotherapy improved PFS compared with very accelerated radiotherapy (0·82, 0·67–0·99; p=0·041). 3-year PFS was 37·6% (95% CI 32·1–43·4) after conventional chemoradiotherapy, 34·1% (28·7–39·8) after accelerated radiotherapy-chemotherapy, and 32·2% (27·0–37·9) after very accelerated radiotherapy. More patients in the very accelerated radiotherapy group had RTOG grade 3–4 acute mucosal toxicity (226 84% of 268 patients) compared with accelerated radiotherapy-chemotherapy (205 76% of 271 patients) or conventional chemoradiotherapy (180 69% of 262; p=0·0001). 158 (60%) of 265 patients in the conventional chemoradiotherapy group, 176 (64%) of 276 patients in the accelerated radiotherapy-chemotherapy group, and 190 (70%) of 272 patients in the very accelerated radiotherapy group were intubated with feeding tubes during treatment (p=0·045). Interpretation Chemotherapy has a substantial treatment effect given concomitantly with radiotherapy and acceleration of radiotherapy cannot compensate for the absence of chemotherapy. We noted the most favourable outcomes for conventional chemoradiotherapy, suggesting that acceleration of radiotherapy is probably not beneficial in concomitant chemoradiotherapy schedules. Funding French Ministry of Health.