This study is to examine the effects on tumors of AZD2171, in the treatment of NSCLC or HNC. The safety and tolerability of AZD2171 will also be studied.

Inclusion Criteria:

• Histologically or cytologically confirmed head and neck cancer (HNC) or unresectable stage IIIb or IV non-small cell lung cancer (NSCLC)
• At least one lesion able to be used for tumor biopsy and to be measured by FDG-PET Scan
• Considered suitable for treatment of NSCLC with no prior biological or immunological therapy for disease
• Or considered suitable for treatment for metastatic or recurrent HNC with no prior biological or immunological therapy for disease

Exclusion Criteria:

• NSCLC: Have received more than 2 previous chemotherapy regimens or have received the last chemotherapy or radiotherapy within 28 days of first dose of AZD2171
• HNC: Previous chemotherapy or radiotherapy if received 28 days of first dose of AZD2171
• Untreatable, unstable brain or meningeal metastases.
• Abnormal liver and kidney blood chemistries
• History of poorly controlled hypertension with resting blood pressure of >150/100
• Recent (< 14 days) major surgery or a surgical incision not fully healed
• Diabetes patients with type I insulin dependent diabetes or poorly controlled type II
• Significant hemorrhage or hemoptysis
• Presence of necrotic/hemorrhagic tumor or metastases