RATIONALE: Drugs used in chemotherapy use different ways to stop cancer cells from dividing so they stop growing or die. It is not yet known whether giving paclitaxel for a shorter period of time is as effective as a standard course of treatment for advanced ovarian cancer.

PURPOSE: Randomized phase III trial to compare the effectiveness of paclitaxel given for 3 months with that of paclitaxel given for 12 months in treating patients who have stage III or stage IV ovarian, fallopian tube, or primary peritoneal cancer.

OBJECTIVES: I. Compare the effect of continuing paclitaxel for 12 months versus 3 months on progression free survival and overall survival in women with advanced ovarian, fallopian tube, or peritoneal cancer who attained complete remission on initial platinum (carboplatin or cisplatin) and paclitaxel based chemotherapy. II. Assess the toxic effects associated with prolonged paclitaxel administration in these patients.

OUTLINE: This is a randomized study. Patients are stratified by stage (optimal stage III vs suboptimal stage III vs stage IV), prior treatments with paclitaxel (over at least 24 hours vs over less than 24 hours), and age (65 and under vs over 65). Patients are randomized to one of two treatment arms. Arm I: Patients receive paclitaxel IV over 3 hours on day 1. Treatment continues every 4 weeks for 3 courses in the absence of disease progression or unacceptable toxicity. Arm II: Patients receive paclitaxel IV over 3 hours on day 1. Treatment continues every 4 weeks for 12 courses in the absence of disease progression or unacceptable toxicity. Patients are followed every 3 months until disease progression or 1 year from registration, then every 6 months for 2 years, and then annually thereafter.

PROJECTED ACCRUAL: A total of 450 patients (225 per arm) will be accrued for this study within 5 years.

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