This open-label, multicenter, randomized study will consist of a Phase Ib: a safety run-in period with 3 ascending doses of E7050 in combination with Cetuximab; and a Phase II portion: a randomized 2-arm period. Approximately 95 patients with Platinum-Resistant Squamous Cell Carcinoma of the head and neck will be enrolled in the study (10-15 patients in the Phase Ib portion and 80 patients in the Phase II portion). Patients will only participate in either the Phase Ib or the Phase II portion of the study.