Background: Most head and neck squamous-cell carcinomas (HNSCCs) are driven by p16INK4A inactivation and cyclin D1 overexpression that results in hyperactivation of cyclin-dependent kinase 4 and 6 (CDK4/6), rather than by the human papillomavirus (HPV). Deregulated cyclin D1 expression also causes resistance to EGFR inhibitors. We previously reported that palbociclib (a selective CDK4/6 inhibitor) given with cetuximab (an EGFR inhibitor) was safe. The aim of this study was to establish the proportion of patients achieving an objective response with palbociclib and cetuximab in recurrent or metastatic HNSCC. Methods: We did a multicentre, multigroup, phase 2 trial to evaluate the activity of palbociclib and cetuximab in platinum-resistant (group 1) and cetuximab-resistant (group 2) HPV-unrelated HNSCC. The study was done across eight university sites in the USA. Eligibility required measurable disease (according to Response Evaluation Criteria in Solid Tumors, version 1·1 [RECIST 1·1]), Eastern Cooperative Oncology Group (ECOG) performance status of 0–2, age of 18 years or older, and disease progression on platinum but cetuximab-naive (group 1) or disease progression on cetuximab (group 2). All patients received palbociclib orally (125 mg/day, on days 1–21) and intravenous cetuximab (400 mg/m2 on cycle one, day 1, then 250 mg/m2 once per week) in 28-day cycles. The primary endpoint was objective response (complete responses and partial responses per RECIST 1·1). Analyses were done per protocol. This trial was registered with ClinicalTrials.gov, NCT02101034, and is ongoing, but both groups are closed to accrual. Findings: Between Oct 19, 2015, and Nov 7, 2018, 62 patients were enrolled onto the trial: 30 patients were enrolled in group 1 and 32 in group 2. Median follow-up was 5·4 months (IQR 4·4–12·1) for group 1 and 5·5 months (4·3–8·3) for group 2. In group 1, of 28 evaluable patients, an objective response was achieved by 11 (39%; 95% CI 22–59). In group 2, of 27 evaluable patients, an objective response was achieved by five (19%; 6–38) in group 2. The most common grade 3–4 palbociclib-related adverse event was neutropenia (in 21 [34%] of 62 patients). No treatment-related deaths occurred. Interpretation: In patients with platinum-resistant or cetuximab-resistant HPV-unrelated HNSCC, palbociclib and cetuximab results in promising activity outcomes. Further studies of CDK4/6 inhibitors are warranted in HPV-unrelated HNSCC. Funding: Pfizer.