This study is designed to evaluate Pemetrexed and Gemcitabine Day 1 followed by Gemcitabine Day 8 every 21 days (Arm A) and Pemetrexed and Gemcitabine Day 1 every 14 days (Arm B) in patients with NSCLC. Each agent and sequence has well demonstrated antitumor activity respectively in patients with locally advanced or metastatic NSCLC. Therefore, it is reasonable to investigate the most optimal schedule for this combination, and which combination is associated with the most anti-tumor activity in the phase II arena.