• To find out how often tumors become smaller or disappear in patients with advanced NSCLC treated with gemcitabine followed by pemetrexed once every 14 days. Chemotherapy treatment will be given for up to 12 times or until the cancer disease increases.
  

• To measure the effects of chemotherapy treatment on:
  
• time until the cancer becomes less;time to cancer re-appears or becomes larger;length of time there is no increase in the amount of cancer;length of time patients survive;
  
• To measure the side-effects from this chemotherapy as given once every 14 days.
  

Inclusion Criteria:

1. Have a diagnosis of advanced stage non-small cell lung cancer.
2. Are able to be active at home and/or work.
3. Have not received chemotherapy for this cancer disease.
4. Have good organ function (for example, most blood work is normal).
5. Have completed any prior radiation treatment at least 4 weeks ago.

Exclusion Criteria:

1. Have been treated with an investigational/research drug within the last month.
2. Have cancer that has spread to the brain and is causing symptoms.
3. Have an active infection or other serious medical condition.
4. Have a second cancer in addition to non-small cell lung cancer.
5. Can not stop taking aspirin or other anti-inflammatory agents for 5-8 days.