This study will determine the maximum tolerated dose and the optimal associated 4 weekly dosing schedule of RO5045337, administered as monotherapy in patients with advanced solid tumors. A first cohort of patients will receive the starting dose of 20mg/m2/day, once daily for 10 days in each 28 day cycle. Subsequent cohorts of patients will receive dose escalations, and possible changes in dosing schedule, based on tolerability and pharmacokinetic knowledge gained from prior treatment cohorts. The anticipated time on study treatment is until disease progression or intolerable toxicity.