The purpose of this study is to test the safety of RAD001 (everolimus) tablets at different dose levels, when added to docetaxel and cisplatin. The investigators want to find out what effects, good and/or bad, that everolimus has when added to docetaxel and cisplatin as treatment for head and neck cancer.

Inclusion Criteria:

• Stage III-IVB head and neck squamous cell carcinoma (HNSCC) or nasopharyngeal cancer (WHO type I, II or III),, previously untreated. Patients with stage II hypopharynx HNSCC will also be eligible. Pathology must be confirmed at MSKCC
• Age ≥ 18 years
• Karnofsky performance status ≥ 70%
• Adequate bone marrow function: Absolute neutrophil count ≥ 1.5 X 109/L, Platelets ≥ 100 x 109/L, Hemoglobin > 10 g/dL.
• Adequate liver function Serum bilirubin must be within the upper limit of normal. (ULN). AST and ALT and Alkaline Phosphatase must be within the range allowing for eligibility
• Adequate renal function: serum creatinine within institutional normal limits, or calculated creatinine clearance (by Cockcroft and Gault method) ≥ 55 mL/min for patients with creatinine limits above institutional normal
• INR < 1.5 or aPTT < 1.5 X upper limits of normal
• Negative urine or serum pregnancy test within 14 days prior to administration of RAD001
• Men and women of childbearing potential must be willing to consent to using effective contraception while on treatment and for at least 3 months thereafter.
• Patients must have ability to understand and the willingness to sign a written informed consent document

Exclusion Criteria:

• Any prior treatment with RAD001, or other agents specifically targeting mTOR
• Any prior radiation therapy for head and neck cancer. Any prior radiation therapy to >25% of the bone marrow. Any prior radiation to whole pelvis and/or brain
• Therapeutic anticoagulation with coumadin (warfarin)
• Hypertriglyceridemia ≥ grade 2 (CTCAE version 3.0)
• Patients who require chronic treatment with steroids ( > prednisone 5 mg/day) or other immunosuppressive agents are excluded. Both cisplatin and RAD001 are immunosuppressive, and chronic steroid use (> prednisone 5 mg/day) or use of other immunosuppressive agents might increase the risk of lethal infection in this setting. Patients on low- dose steroid replacement regimens (≤ prednisone 5 mg/day) are not excluded, because low dose steroids should not be immunosuppressive
• Impairment of gastrointestinal function or gastrointestinal disease that may significantly alter the absorption of RAD001 (e.g., ulcerative disease, uncontrolled nausea, vomiting, diarrhea, malabsorption syndrome or small bowel resection)
• Active infection or serious underlying medical condition that would impair the patient's ability to receive protocol treatment. Other concurrent severe and/or uncontrolled medical disease which would compromise participation in the study in the opinion of the investigator (e.g., uncontrolled diabetes, unstable angina, or congestive heart failure - New York Heart Association Class III or IV)
• HIV-positive patients. These patients are at increased risk of lethal infections when treated with marrow suppressive therapy. Additionally, pharmacokinetic interactions between antiretroviral therapy and the study regimen may be problematic for these patients
• Women who are pregnant or lactating
• Other active malignancy, other than indolent malignancies which the investigator determines are unlikely to interfere with treatment and safety analysis. For example, patients with non-melanoma skin cancer, in situ carcinoma of the cervix, or prostate cancer with no current biochemical (PSA) or radiologic evidence of disease may enroll
• Patients with hearing loss requiring hearing aid or intervention (i.e. interfering in a clinical significant way with activities of daily living).
• Patients with multifocal peripheral sensory alterations or paresthesias (including tingling) interfering with function, per patient report (example: activities of daily living)
• Impaired lung function: O2 saturation 88% or less at rest on room air by Pulse Oximetry. If O2 saturation is ≤ 88% at rest, further pulmonary function tests (PFTs) should be ordered to confirm normal pulmonary function and eligibility
• Patients should not receive immunization with attenuated live vaccines within one week of study entry or during the study period. Close contact with those who have received attenuated live vaccines should be avoided during treatment with everolimus. Examples of live vaccines include intranasal influenza, measles, mumps, rubella, oral polio, BCG, yellow fever, varicella, and TY21a typhoid vaccines
• Liver disease such as cirrhosis or severe hepatic impairment (Childs-Pugh class C)