 This study is being carried out to assess if adding ZD6474 to best supportive care BSC is more effective than best supportive care alone, for the treatment of patients with non-small cell lung cancer, whose disease has recurred after previous chemotherapy and an Epidermal Growth Factor Receptor Tyrosine Kinase Inhibitor EGFR TKI. ZD6474 is a new anti-cancer drug in development that works in a different way to standard chemotherapy drugs. It targets the growth of new blood vessels to a tumour and thereby might slow the rate at which the tumour may grow. Early studies indicate that ZD6474 has a positive effect on the time that a tumour may take to progress to a further stage. Approximately 930 patients will take part in this study. It will be conducted in hospitals and clinics in North and South America, Europe and Asia. 