 This is a multicenter, open-label all people know the identity of the intervention, randomized study medication is assigned by chance, Phase 3 study comparing the combination of trabectedin DOXIL with DOXIL monotherapy in patients with advanced ovarian cancer who were previously treated and for whom first-line platinum-based chemotherapy regimen has failed. Approximately 650 patients will be randomly assigned to 1 of the treatment arms DOXIL and DOXIL trabectedin over 2 years. At the time of randomization, patients will be stratified on the basis of platinum sensitivity of disease sensitive or resistant and baseline Eastern Cooperative Oncology Group performance status score 0 to 1 or 2. Safety will be evaluated on the basis of adverse events, clinical laboratory tests, physical examination, vital signs assessment and cardiovascular safety assessment. An interim analysis of overall survival will be performed in conjunction with progression-free survival analysis during the study. Treatment will be continued until disease progression occurred or until patients experienced a confirmed complete response for at least 2 cycles. Continuation of treatment in select individual patients beyond this study end date will be allowed if the investigator determined that the patient is benefiting from treatment, is eligible to receive further therapy, and consents to treatment. If disease progression has not occurred at treatment termination, then disease assessment will continue every 8 weeks until there is evidence of disease progression or death, or until the clinical data cutoff date, or until the start of first subsequent anticancer therapy, whichever is earlier. 