 This study will determine the maximum tolerated dose and pharmacokinetic profile of R1507 in patients with metastatic or locally advanced malignant solid tumors, non-Hodgkins lymphoma or Hodgkins lymphoma. Groups of patients will be sequentially enrolled to receive ascending doses of R1507 either weekly or three-weekly by intravenous infusion. The starting dose of 1mgkg iv for each dosing regimen will be escalated in subsequent groups of patients after a satisfactory assessment of safety, tolerability and pharmacokinetics of the previous dose. The anticipated time on study treatment is until disease progression or dose-limiting toxicity, and the target sample size is 100 individuals. 