OUTLINE: This is two-stage, partially randomized study. In stage one, patients are randomized to arm I or II. Arm I: Patients receive vaccinia-carcinoembryonic antigen (CEA) vaccine intradermally on day 1 of course 1 and ALVAC-CEA vaccine (CEA-Avipox vaccine) intramuscularly (IM) on day 1 of courses 2-4. Each course lasts 28 days. Arm II: Patients receive ALVAC-CEA vaccine (CEA-Avipox vaccine) IM on day 1 of courses 1-3 and vaccinia-CEA vaccine intradermally on day 1 of course 4. Each course lasts 28 days. Patients in arms I and II continue 28-day courses through month 6 and then receive 3-month courses for 2 years in the absence of disease progression or unacceptable toxicity. In stage two, patients are enrolled successively into arms III and IV. Arm III: Patients receive vaccines according to whichever schedule (arm I or II) was found to be superior plus sargramostim (GM-CSF) subcutaneously (SC) on days 1-4 of each course. Each course lasts 28 days. Arm IV: Patients receive vaccines plus GM-CSF as in arm III and interleukin-2 SC once daily on days 7-11 of each course. Each course lasts 28 days. Patients on arms III and IV continue 28-day courses through month 6 and then receive 3-month courses for 2 years in the absence of disease progression or unacceptable toxicity. If 2 or more patients in either arm III or IV experience dose limiting toxicity, accrual into study stops. Otherwise, the best response among the 4 arms is determined and further HLA-A2 positive patients are enrolled into that arm so that a total of 6 HLA-A2 positive patients with advanced disease and 6 HLA-A2 positive patients with NED (without radiographic or clinical evidence of tumor) are treated. If more than one regimen is equally superior, the least toxic regimen is chosen for further accrual. Patients are followed at 28 days following the last vaccination.