Pemetrexed Plus Cisplatin as First-Line Treatment in Stage IV or Recurrence of Gastric Cancer

Inclusion Criteria: * Histologically confirmed diagnosis of adenocarcinoma of the gastric. Stage IV disease, not amenable to curative surgery, or disease recurrence after prior surgery. * Disease status must be that of measurable disease with presence of at least one measurable lesion as defined by Response Evaluation Criteria in Solid Tumors (RECIST) criteria. * In bidimensionally measurable lesions the longest diameter should be selected for measurement. * Tumor lesions in areas of prior radiation therapy may be included only if they were clearly progressing. * If only a single lesion is present in a patient who had prior therapy for gastric adenocarcinoma, the neoplastic nature of the lesion should be confirmed by cytology and/or histology. * Ultrasound and clinical examination are not allowed for assessment of measurable disease. * Elevation of tumor markers, pleural or pericardial effusion, ascites, bone lesions, cystic lesions, or carcinomatous lymphangitis pulmonis/cutis is defined as not being measurable. * Performance Status of 0 or 1 on the Eastern Cooperative Oncology Group (ECOG) Scale. * Estimated life expectancy of at least 12 weeks. * No prior chemotherapy or radiotherapy. * Patient compliance and geographic proximity that allow adequate follow-up. Adequate organ function including the following: * Bone marrow: absolute neutrophil count 1.5 x 10 to the ninth power/liter (L), platelets 100 x 10 to the ninth power/L, hemoglobin \>=9 grams per deciliter (g/dL). * Hepatic: bilirubin \<=1.5 x upper limit of normal (ULN); alkaline phosphatase, aspartate transaminase and alanine transaminase \<=3.0 x ULN. * Renal: Calculated creatinine clearance \>=45 milliliters (ml)/minute. * Men or women, age 18 to 70 years. * For women: Must be surgically sterile, post-menopausal, or compliant with a medically approved contraceptive regimen during and for 3 months after the treatment period; must have a negative serum or urine pregnancy test within 7 days before study enrollment and must not be breast-feeding. * For men: Must be surgically sterile, or compliant with a contraceptive regimen during and for 3 months after the treatment period. * Signed informed consent from patient. Exclusion Criteria: * Have received treatment within the last 30 days with a drug that has not received regulatory approval for any indication at the time of study entry. * Concurrent administration of any other tumor therapy. * Active infection. * Serious concomitant disorders that would compromise the safety of the patient or compromise the patient's ability to complete the study, at the discretion of the investigator. * Pregnancy. * Breast-feeding. * History of significant neurological or mental disorder, including seizures or dementia. * Have had a prior malignancy other than gastric cancer, carcinoma in situ of the cervix, or nonmelanoma skin cancer, unless that prior malignancy was diagnosed and definitively treated at least 5 years previously with no subsequent evidence of recurrence. * Patients with a history of low grade (Gleason score less than or equal to 6) localized prostate cancer will be eligible even if diagnosed less than 5 years previously. * Inability to interrupt aspirin or other nonsteroidal anti-inflammatory drugs 2 days before, the day of, and 2 days after the dose of pemetrexed plus cisplatin. * If a patient is taking a nonsteroidal anti-inflammatory drug (NSAID) or salicylate with a long half-life it should not be taken 5 days before, the day of, and 2 days after the dose of pemetrexed plus cisplatin. * Clinically significant ascites or pleural effusion that is apparent at clinical examination and cannot be controlled by drainage or other procedures prior to study enrollment. NOTE: Small effusions noted on computed tomography (CT) scan do not exclude the patient from study enrollment. * Inability or unwillingness to take folic acid, vitamin B12 supplementation, or dexamethasone. * Known or suspected brain metastasis. Patients who have clinical signs or symptoms that are suspicious of brain metastasis must have a pretreatment CT or magnetic resonance imaging (MRI) of the brain. A patient with documented brain metastasis, at the time of consideration for study entry or in the past, will be excluded from entering in the study.