This study is a multicentre, open label, non-comparative, two stage phase II trial to assess the activity of ZD1839 (IRESSA) in patients with malignant mesothelioma. Patients will receive trial treatment as first-line therapy, administered continuously once daily until the completion of six 4-week cycles of treatment, disease progression, unacceptable toxicity or withdrawal of consent. Patients continuing to show evidence of response, disease stabilization or clinical benefit from ZD1839 may continue to receive therapy beyond completion of the trail.