 The primary objectives of the study are 1. to assess the efficacy of continuous hepatic arterial infusion HAI of FUDR and dexamethasone DEX in patients with unresectable hepatocellular carcinoma HCC and intrahepatic cholangiocarcinoma ICC and 2.to assess patient tolerability of this therapy stratified by degree of underlying hepatic parenchymal disease, as determined on liver biopsy. Secondary objectives are 1. to use dynamic MRI to evaluate changes in tumor perfusion during treatment and to correlate these findings with radiographic tumor response and 2. to investigate molecular genetic changes associated with these tumors using comparative genomic hybridization and cDNA array from tumor and liver biopsy specimens obtained at the time of operation. All patients enrolled in the study will begin HAI FUDR at 0.16 mgkgday. An initial cohort of 12 patients will be enrolled and treated. Dose limiting toxicity DLT related to FUDR is defined by changes in liver function blood tests that are unrelated to disease progression or mechanical biliary obstruction. Modifications in the FUDR dose may be required. A patient will be considered intolerant of therapy if treatment must be stopped due to DLT at least once during the first 3 months. Treatment will continue as long as there is at least stable disease and acceptable toxicity. 