 This study hopes to evaluate whether the combination of Gemzar plus Alimta will have any beneficial effects for patients with recurrent platinum-sensitive or platinum-resistant ovarian or peritoneal cancer. Treatments are weekly for two weeks, with the 3rd week off and will be repeated every 21 days. Side effects and the overall safety of the treatment will also be monitored and evaluated. In addition, a Quality of Life questionnaire is part of this study to help measure patient perceived benefits or drawbacks to this treatment regimen. 