This study will evaluate the pharmacokinetics, maximum tolerated dose and anti-tumor activity of RO5083945 in patients with metastatic and/or locally advanced malignant EGFR+ solid tumors. In the first part of the study, groups of patients will be sequentially enrolled to receive ascending doses of RO5083945 administered weekly, every 2 weeks or every 3 weeks. The starting dose of 50mg weekly will be escalated in subsequent groups of patients after a successful assessment of the safety, tolerability and pharmacokinetics of the previous dose. In Part 2 of the study, patients with EGFR+ and mutant KRAS colorectal cancer will be enrolled, and will receive RO5083945 at the recommended dose and regimen identified in Part 1. The anticipated time on study treatment is until disease progression, and the target sample size is <100 individuals.