Background: – Alveolar soft part sarcoma is a rare type of tumor that has a lot of blood vessel growth. Cediranib and sunitinib are two cancer treatment drugs that work by blocking the growth of new blood vessels. This may help to stop tumor growth. Some patients with alveolar soft part sarcoma treated with cediranib or sunitinib had tumors that either decreased in size or remained stable without growth for a long time. More research is needed to see whether these drugs can be approved as a standard treatment for alveolar soft part sarcoma. Objectives: – To test the safety and effectiveness of cediranib and sunitinib to treat alveolar soft part sarcoma. – To determine the objective response rate of cediranib and sunitinib in patients with alveolar soft part sarcoma. Eligibility: – Individuals at least 16 years of age who have alveolar soft part sarcoma. – Individuals who have not received prior cediranib or sunitinib. Design: – All participants will be screened with a physical exam and medical history. They will also have blood and urine tests, tumor imaging studies, and biopsies. – Participants will be divided into two groups: one group will start with cediranib and the other will start with sunitinib. – During Part I of the study, participants will take cediranib or sunitinib by mouth once a day. They will continue this routine every day for 28 days (one cycle of treatment). They will stop taking the drug if the side effects become too severe or the tumor starts growing again. – Participants will not have any cancer treatment for 2 weeks before starting Part II. – During Part II, participants will receive the other study drug (cediranib or sunitinib). However, if one of the drugs is not effective or its side effects are too severe, participants will not receive the drug and will stop being in the study. – Participants will be monitored with frequent blood and urine tests. They will also have tumor imaging studies and other tests.