DISEASE CHARACTERISTICS:

• Histologically confirmed seminoma or nonseminoma germ cell cancer

  • Male patients only
  • Females with dysgerminoma or other germ cell cancers are eligible but will not be included in the primary analysis

• Tumor-free but remain at high risk OR meeting 1 of the following criteria:

  • Marker negative after chemotherapy with surgical resection of residual cancer (s-CR)*

  • Chemo-responsive first relapse*

    • Patients in first relapse responding to second-line therapy with a taxane- or non-taxane-based regimen

      • Paclitaxel plus ifosfamide-based regimen
      • Non-paclitaxel plus ifosfamide-based regimen

  • All other patients meeting the following criteria:

    • Second relapse
    • Responding to third-line therapy
    • No history of absolute refractoriness to platinum-based therapy NOTE: *Patients with mediastinal primary nonseminomatous germ cell cancer (NSGCT) are eligible provided they are not in subsequent relapse and not refractory to first-line therapy.
• Evaluable disease (measurable by radiographic study and/or serum tumor marker elevation)

• History of CNS metastases allowed provided the patient has been treated and off steroids with stable post-radiotherapy neurological status for at least 1 month and seizure-free for at least 1 month with therapeutic anticonvulsant levels prior to registration

  • The presence of peripheral neuropathy will not be an absolute contraindication but should be discussed with the principal investigator

PATIENT CHARACTERISTICS:

• Karnofsky performance status 70-100%
• Creatinine clearance ≥ 60 mL/min
• Bilirubin ≤ upper limit of normal (ULN) (or indirect bilirubin ≤ 2.5 times ULN if the patient has Gilbert syndrome)
• ALT and AST ≤ 3 times ULN (no liver involvement) or ≤ 4 times ULN (if liver involvement)
• ANC ≥ 1,500/μL
• Platelets ≥ 120,000/μL
• Hemoglobin ≥ 10 g/dL (may be transfused or receive epoetin alfa, but may not be treated with colony-stimulating factors or platelet transfusions)
• Ejection fraction normal by MUGA or echocardiogram

• No prior invasive malignancy except for adequately treated nonmelanoma skin cancer or other cancers from which the patient has been disease-free for at least 5 years

  • Prior hematologic malignancies are excluded
• No EKG evidence of active cardiac disease (i.e., arrhythmias or ischemia) that would contraindicate the administration of etoposide and paclitaxel
• Room air PaO_2 ≥ 70 mm Hg

• FEV_1 ≥ 2 liters or 75% of lower limit of predicted value

  • No history of clinically significant bleomycin-associated or other serious lung disease
• HIV negative
• Patients with seropositivity for hepatitis B surface antigen or hepatitis C antibody must have a liver biopsy showing no evidence of active hepatitis or cirrhosis
• Must have recovered from major infections and, in the opinion of the investigator, not have significant active medical illness precluding protocol treatment or survival

PRIOR CONCURRENT THERAPY:

• See Disease Characteristics
• Recovered from prior surgery
• No expected need for radiotherapy during the protocol treatment period