Iressa and Taxotere Study in Patients With Metastatic Urothelial Cancer

Inclusion Criteria: * All patients must have histologic demonstration of metastatic or locally unresectable transitional cell carcinoma of the urothelium. Minor components (\<50% overall) of variants such as glandular or squamous differentiation, or evolution to more aggressive phenotypes such as sarcomatoid of small cell change are acceptable. However, when these atypical histologies are dominant, other treatment approaches may be appropriate, and such patients are not eligible. * All patients must have demonstrated some objective response to combination chemotherapy, and be clinically without progression since this response was appreciated. In general, patients will have been treated with at least two successive combination regimens in order to achieve maximum benefit from available chemotherapy. * Patients who have not achieved a complete response to therapy must have received one of the chemotherapy regimens outlined in Appendix D prior to receiving consolidation therapy. Exceptions to this generalization would include patients with a near complete response to the first regimen given, or patients that are not fit for aggressive chemotherapy beyond an initially used regimen to which they responded. Patients must begin "consolidation" therapy within 6 weeks of the end of the last cycle of induction chemotherapy, and should begin as soon as possible. * Zubrod performance status of 3 or better. If PS = 3 this must, in the opinion of the investigator, be secondary to the effects of induction chemotherapy and not the underlying cancer. * Patients with a history of cardiac disease, or an ejection fraction (EF) less than 50% at the time of initiation of chemotherapy, must be demonstrated to have an ejection fraction of at least 40%. In addition, patients having received more than 250 mg/m\^2 of doxorubicin during their induction phase, or who have EKG changes since initiation of chemotherapy must have an EF of at least 45%. Patients with no history of cardiac disease, a normal EKG and no more than 250 mg/m\^2 of doxorubicin are not required to have an EF measurement. * Provision of written informed consent. * Women of childbearing potential must be willing to practice acceptable methods of birth control to prevent pregnancy. * Males taking ZD1839 must also use birth control while taking the drug to avoid pregnancy in their partner. * International normalized ratio (INR) elevations, bleeding, or both events have been reported in some patients taking warfarin. Patients taking warfarin with a target INR of \> or = 2, should be monitored regularly (every week in the first cycle, with further monitoring based on the experience in the first cycle) for changes in prothrombin time (PT) or INR. Patients on prophylactic low dose warfarin (ie: 1-2 mg qd for central line thrombosis prophylaxis) do not require frequent monitoring. Exclusion Criteria: * Predominantly small cell histology. * AST or conjugated bilirubin greater than twice the upper limit of normal. * Serum creatinine greater than 2.5 mg/dL , or a creatinine clearance (either measured or estimated by Cockcroft formula) of less than 25 mL/min: creatinine clearance (CLcr) = \[(140-age) x wt(kg)\]/\[72 xCreat (mg/dL)\] (Multiply by 0.85 for females) * Absolute neutrophil count (ANC) less than 1,000; Platelets less than 75,000. * Prior (lifetime) cumulative exposure to doxorubicin greater than 400 mg/m\^2. * Pregnant and lactating women are excluded. Women of childbearing potential must have a negative pregnancy test prior to starting therapy. * An active, or likely to become active, second malignancy. * Known severe hypersensitivity to ZD1839 or any of the excipients of this product. * Concomitant use of phenytoin, carbamazepine, barbiturates, rifampin, phenobarbital of St. John's Wort * Treatment with a non-approved or investigational drug within 30 days before Day 1 of trial treatment. * Incomplete healing from previous oncologic or other major surgery * Note that there is no requirement for measurable or evaluable disease. Evaluation of response to therapy is not an endpoint of this trial. * Prior treatment with therapy which specifically targets the HER family of receptors. * Patients with peripheral neuropathy \> or = to grade 2 should be excluded. Patients may be included if their neuropathy has resolved to grade 1 by the time they are registered on the protocol. * Evidence of any other significant clinical disorder or laboratory finding that makes it undesirable for the subject to participate in the trial. * As judged by the investigator, any evidence of severe or uncontrolled systemic disease (e.g., unstable or uncompensated respiratory, cardiac, hepatic or renal disease). * Any evidence of clinically active interstitial lung disease (patients with chronic stable radiographic changes who are asymptomatic need not be excluded).