S9701 Paclitaxel in Treating Patients With Advanced Ovarian, Fallopian Tube, or Primary Peritoneal Cancer in Remission

DISEASE CHARACTERISTICS: Histologically confirmed advanced ovarian epithelial, fallopian tube, or primary peritoneal cancer Must have undergone an initial exploratory laparotomy with tumor debulking AND Must be FIGO stage IIIA, IIIB, IIIC, or IV at the time of initial laparotomy Must have attained a clinically defined complete remission (CR) following treatment with platinum (cisplatin or carboplatin) and paclitaxel based combination chemotherapy regimen by achieving the following: No evidence of cancer on physical examination CA-125 no greater than 35 units/mL Creatinine no greater than 2.0 mg/dL OR Creatinine clearance greater than 60 mL/min Bilirubin no greater than 2.0 mg/dL Negative ascites No evidence of residual cancer on CT scan of the abdomen/pelvis or chest x-ray (or chest CT scan, if performed) No symptoms felt to be secondary to persistent malignancy Must have received a minimum of 5 and a maximum of 6 courses of chemotherapy prior to study Must register for study within 21 to 56 days after prior chemotherapy Not concurrently registered to SWOG-S9618, SWOG-S9619, SWOG-S9912, or SWOG-S0009 or front line treatment phase III GOG trials PATIENT CHARACTERISTICS: Age: Any age Performance status: SWOG 0-2 Life expectancy: Not specified Hematopoietic: Granulocyte count at least 1,200/mm3 Platelet count at least 100,000/mm3 Hepatic: See Disease Characteristics Renal: See Disease Characteristics Other: No prior malignancy within past 5 years except adequately treated basal cell or squamous cell skin cancer, carcinoma in situ of the cervix, or incidental carcinoid PRIOR CONCURRENT THERAPY: Biologic therapy: No concurrent antitumor treatment No concurrent immunotherapy Chemotherapy: See Disease Characteristics Recovered from prior chemotherapy Prior cisplatin allowed if initial dose at least 50 mg/m2 Prior carboplatin allowed if initial dose at least 300 mg/m2 or AUC at least 4 No other concurrent chemotherapy Endocrine therapy: No concurrent hormonal therapy Radiotherapy: No concurrent radiotherapy No prior abdominal/pelvic irradiation Surgery: See Disease Characteristics No second look laparotomy or laparoscopy