The purpose of this Phase I study is to find the largest dose of the drug irinotecan, in combination with ZD1839, that can be given safely to children and to learn the good and bad effects. Studies performed in the laboratory have shown that ZD1839 helps make available the orally administered irinotecan. In this study the intravenous (given into the vein) formula of irinotecan will be given orally on days 1-5 and days 8-12. The dose of ZD1839 will be a fixed dose and will be administered orally on days 1-12. 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.