In this study the intravenous formulation of irinotecan will be given orally on days 1-5 and days 8-12 (dose level begins at 5 mg/m2 ). One patient will be treated at each dose level of irinotecan until moderate toxicity is observed. At the level where moderate toxicity is observed, the cohort size will be increased to 2 patients. Dosages will then be increased until the development of DLT as guided by the EWOC model. The estimated MTD will be continually reassessed using all data from preceding patients. The toxicity data of all patients enrolled in the trial are used to update the dose-toxicity relationship and to guide the next escalation/de-escalation. The calculation will be carried out with EWOC software. Patients will be enrolled and the dose assigned is determined based on previous participants' toxicity. The dose of ZD1839 will be a fixed dose and will be administered orally on days 1-12 - [150 mg/m2 (maximum 250 mg)] Each course of treatment will consist of 21 days. The administration of irinotecan on day 12 of course 1 and day 2 of course 2 will be an intravenous administration. All other doses and subsequent courses will consist of an orally administered dose.