The purpose of this clinical research study is to learn if vinflunine can shrink or slow the growth of the cancer or increase survival in patients with transitional cell carcinoma of the urothelium. The safety of this treatment will also be studied.

Inclusion Criteria:

• Clinical diagnosis of transitional cell carcinoma of the urothelium that is locally advanced or metastatic (i.e. patients cannot be candidates for local/regional control of disease).
• Relapse or progression within 12.5 months of prior cisplatin or carboplatin containing chemotherapy regimen.
• Adequate performance status (Karnofsky greater or equal to 80).

Exclusion Criteria:

• Receipt of more than 1 prior chemotherapy regimen in any setting.
• Prior discontinuation of platinum due solely to toxicity.
• Current neuropathy greater or equal to CTC grade 2.
• Prior radiation to greater or equal to 30% of bone marrow.
• Inadequate hematologic function: ANC <1,500 cells/mm3, Platelet<100,000 cells/mm3.
• Inadequate hepatic function: total bilirubin > 1.5 times ULN, ALT/AST > 2.5 times ULN or > 5 times ULN in case of liver metastasis.
• Inadequate renal function: creatinine clearance <20 ml/min.
• Prior allergy to any vinca-alkaloid.