Inclusion Criteria:

- Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1

- Patients must have pathological evidence of persistent lymph node disease with viable
tumor cells following primary concurrent chemoradiotherapy of locoregionally advanced
(stage III/IV) head and neck squamous cell carcinoma (HNSCC) of the oral cavity,
oropharynx, larynx, or hypopharynx; persistent lymph node disease with viable tumor
cells will be determined by the histological determination of tumor viability defined
as tumor cells with intact cellular compartments (i.e. cytoplasm and nucleus) that do
not exhibit karyolysis, pyknosis, or karyorrhexis on hematoxylin and eosin (H&E)
staining

- Patients must have undergone a neck dissection following completion of
chemoradiotherapy and must have involved at the minimum a compartment dissection of
nodal levels with residual abnormalities on post-treatment imaging studies

- Patients must have achieved a complete response at the primary disease site after
chemoradiotherapy

- All persistent lymph node disease must have received at least 66 Gy of radiotherapy
and must have been completely surgically resected prior to registration, and surgical
incisions should be adequately healed

- Patients with extracapsular lymph node extension will be eligible

- Patients must be at least 6 weeks (42 days) and no more than 16 weeks (112 days) from
completion of chemoradiation at the time of registration

- Patients will be eligible regardless of ability to swallow; patients with dysphagia
may have afatinib/placebo administered via gastrostomy tube

- Absolute neutrophil count >= 1,000/mm^3

- Platelets >= 100,000/mm^3

- Total bilirubin =< 1.5 x the upper limit of normal (ULN)

- Aspartate amino transferase (AST) =< 3 x the ULN

- Alanine amino transferase (ALT) =< 3 x the ULN

- Calculated creatinine clearance must be >= 50 ml/min using the Cockcroft-Gault
formula

- Patients with known persistent disease at the primary mucosal site (even if resected
after chemoradiotherapy), distant metastatic disease or with any gross residual
disease following neck dissection will not be eligible

- Patients with known hypersensitivity to afatinib or any of the excipients of this
product will be excluded

- Prior cetuximab or any epidermal growth factor receptor (EGFR) inhibitors will not be
permitted including cetuximab administered with a chemoradiotherapy or radiotherapy
regimen

- As all patients in this study will have received prior full dose, curative-intent
external-beam radiotherapy to the involved neck, no additional external-beam
radiotherapy will be permitted prior to or during study participation

- No prior adjuvant chemotherapy (aside from the initial induction chemotherapy
followed by chemoradiotherapy or chemoradiotherapy regimen) will be permitted

- Patients with history of acute myocardial infarction within 3 months prior to
registration, and any history of uncontrolled angina, uncontrolled arrhythmia, or
uncontrolled heart failure will be excluded

- Women must not be pregnant or breast-feeding due to potential harm to the fetus and
baby by afatinib; all females of childbearing potential must have a blood test or
urine study within 2 weeks prior to registration to rule out pregnancy; a female of
childbearing potential is any woman, regardless of sexual orientation or whether they
have undergone tubal ligation, who meets the following criteria: 1) has not undergone
a hysterectomy or bilateral oophorectomy; or 2) has not been naturally postmenopausal
for at least 24 consecutive months (i.e., has had menses at any time in the preceding
24 consecutive months)

- Women of childbearing potential and sexually active males must be strongly advised to
use an accepted and effective method of contraception

- Patients with active infections, other cancers, or history of other cancers will be
excluded

- Patients participating in any other clinical trials or taking any other experimental
medications will be excluded