Topotecan and Gefitinib (Iressa) for Ovarian, Peritoneal, or Fallopian Tube Cancer

The purposes of this study are: 1. To determine the dose limiting toxicity (DLT) and the maximum tolerated dose (MTD) weekly of topotecan in combination with standard dose gefitinib in patients with relapsed, platinum-resistant, ovarian, peritoneal or fallopian tube cancers that are epidermal growth factor receptor (EGF-R) positive (\>/= 1+). 2. To determine the response rate and response duration in this patient population treated with the maximum tolerated dose (MTD) of topotecan administered on a weekly schedule in combination with standard dose gefitinib, given by way of the mouth (PO) daily.