During the follow-up, the patients are followed between the end of week 4 and week 6 by clinical and biological evaluation. Evaluation of tumor sites under sunitinib is planned every 2 cycles with CT scans. For patients with anaplastic or differentiated thyroid carcinoma, the first stage will include 21 efficacy-evaluable patients. An additional 29 efficacy-evaluable patients will be included at the second stage.