This phase 1b, open-label trial assessed the combination of afatinib, an ErbB family blocker, with cetuximab, an epidermal growth factor receptor (EGFR) monoclonal antibody, in heavily pretreated patients with unselected/EGFR wild-type, advanced solid tumours. In Part A, the maximum tolerated dose (MTD) of afatinib + cetuximab was evaluated using a 3 + 3 dose-escalation design; the starting dose was afatinib 30 mg/day plus cetuximab 250 mg/m/week (after cetuximab 400 mg/m loading dose), escalating to afatinib 40 mg/day. Part B further evaluated safety and tolerability at the MTD and preliminary anti-tumour activity in three patient cohorts with squamous non-small cell lung cancer (NSCLC), head and neck squamous cell carcinoma (HNSCC) and other solid tumours. Nine patients were treated in Part A; the MTD and recommended dose was determined as afatinib 40 mg/day plus cetuximab 250 mg/m/week. In Part B, 49 patients were treated at the recommended dose (12 with squamous NSCLC, 15 with HNSCC and 22 with other tumours). The most common treatment-related adverse events (AEs) across all 58 patients were diarrhoea (63.8%) and acneiform dermatitis (43.1%). Overall, the best confirmed response was stable disease (SD; 53.4%); mean duration of disease control was 4.5 months; median progression-free survival was 2.6 months. In Part B, 55.1% of patients had SD (squamous NSCLC, 75.0%; HNSCC, 66.7%; other tumours; 36.4%). In conclusion, the recommended phase 2 dose was determined as afatinib 40 mg/day plus cetuximab 250 mg/m/week. AEs were predictable and manageable, and anti-tumour activity was observed in some patients, particularly in those with squamous NSCLC and HNSCC. CLINICAL TRIAL REGISTRATION: ClinicalTrials.gov NCT02020577.