This is an open-label, dose-escalating Phase I study of ON 01910.Na in patients with advanced cancers, who have satisfied the inclusion/exclusion criteria enumerated in this protocol. Patients will receive ON 01910.Na intravenously by 24 hour continuous infusion once every week (3 weeks per cycle), until evidence of disease progression, intolerable adverse events, or withdrawal of patient consent. Safety monitoring will be done for at least 3 weeks before escalation to the next dose level. As of Amendment 7, up to 6 patients with gynecological malignancies will be enrolled at the 2400 mg/m2 dose level to determine the appropriateness of this dose as the Recommended Phase Two Dose (RPTD).