-  INCLUSION CRITERIA:

          -  Participants must have histologically confirmed thymoma or thymic carcinoma by the
             pathology department/CCR/NCI.

          -  Participants must have had at least one prior line of platinum-based chemotherapy or
             participant must have refused cytotoxic chemotherapy. Progressive disease must be
             documented prior to study entry and participants must have advanced, unresectable
             disease that is not amenable to surgical resection.

          -  Prior treatment of PD-1 or PD-L1-directed immune checkpoint blockade is permitted if
             treatment was not discontinued due to disease progression or lifethreatening adverse
             events per the investigators discretion (laboratory abnormalities alone with prior
             therapy will not exclude participants from this trial).

          -  Disease must be measurable with at least 1 unidimensional measurable lesion by RECIST
             1.1.

          -  Male or female subjects aged greater than or equal to 18 years

             -- Because no dosing or adverse event data are currently available on the use of
             Avelumab in participants <18 years of age, children are excluded from this study, but
             will be eligible for future pediatric trials.

          -  ECOG performance status less than or equal to 1.

          -  Participants must have normal organ and marrow function as defined below:

               -  absolute neutrophil count: greater than or equal to 1,500/mm^3 OR greater than or
                  equal to 1.5 x 10^9/L

               -  platelets greater than or equal to 100,000/mm^3 OR greater than or equal to 100 x
                  10^9/L

               -  hemoglobin greater than or equal to 9g/dL (may have been transfused)

               -  total bilirubin less than or equal to 1.5 x the upper limit of normal range(ULN)

               -  AST(SGOT)/ALT(SGPT) less than or equal to 2.5 x ULN OR less than or equal to 5 x
                  ULN for subjects with documented metastatic disease to the liver

               -  creatinine clearance greater than or equal to 30 mL/min according to the
                  Cockcroft Gault formula (or local institutional standard method)

          -  Highly effective contraception for both male and female subjects if the risk of
             conception exists. (Note: The effects of the study drug on the developing human fetus
             are unknown. Thus, women of childbearing potential and men must agree to use highly
             effective contraception, defined as 2 barrier methods, or 1 barrier method with a
             spermicide, an intrauterine device or use of oral female

        contraceptive. Effective contraception must be used 30 days prior to first study drug
        administration, for the duration of trial participation, and at least for 30 days after
        last avelumab treatment administration if the risk of conception exists. Should a woman
        become pregnant or suspect she is pregnant while she or her partner is participating in
        this trial, the treating physician should be informed immediately.)

        -Pregnancy test: negative serum or urine pregnancy test at screening for women of
        childbearing potential.

        EXCLUSION CRITERIA:

          -  Concurrent treatment with a non-permitted drug

          -  Concurrent anticancer treatment within 28 days before the start of trial treatment
             (e.g., cytoreductive therapy, radiotherapy [with the exception of palliative bone
             directed radiotherapy], immune therapy, or cytokine therapy except for
             erythropoietin); major surgery within 28 days before the start of trial treatment
             (excluding prior diagnostic biopsy); concurrent systemic therapy with
             immunosuppressive agents within 28 days before the start of trial treatment; use of
             hormonal agents for the treatment of thymic cancer within 7 days before the start of
             trial treatment; or use of any investigational drug within 28 days before the start of
             trial treatment.

             --Note: Subjects receiving bisphosphonate or denosumab are eligible provided treatment
             was initiated at least 14 days before the first dose of avelumab.

          -  History of previous malignant disease within the last 2 years with the following
             exceptions: basal or squamous cell carcinoma of the skin, cervical carcinoma in situ,
             ductal carcinoma in situ of the breast, papillary or follicular thyroid carcinoma, and
             non-muscle invasive bladder cancer.

          -  Active autoimmune disease that might deteriorate when receiving an immune-stimulatory
             agent. Participants with diabetes type 1, vitiligo, psoriasis, pure red cell aplasia,
             Good s syndrome or hypo- or hyperthyroid diseases not requiring immunosuppressive
             treatment are eligible. Anti-acetylcholine receptor and anti-striated muscle
             antibodies will be checked during screening. Participants will be ineligible if
             results are positive, even if there is no clinical history of autoimmune disease.

          -  Participants with symptomatic brain metastases will be excluded from trial secondary
             to poor prognosis. However, participants who have had treatment for their brain
             metastasis and whose brain disease has remained stable for 3 months without steroid
             therapy may be enrolled.

          -  Active infection requiring systemic therapy or significant acute or chronic infections
             including, among others:

               -  Hepatitis B virus (HBV) or hepatitis C virus (HCV) infection at screening
                  (positive HBV surface antigen or HCV RNA if anti-HCV antibody screening test
                  positive).

               -  Known history of testing positive for HIV or known acquired immunodeficiency
                  syndrome.

          -  Prior organ transplantation including allogenic stem-cell transplantation.

          -  Known prior severe hypersensitivity to investigational product or any component in its
             formulations, including known severe hypersensitivity reactions to monoclonal
             antibodies (NCI CTCAE v4.03 Grade greater than or equal to 3).

          -  Persisting toxicity related to prior therapy (NCI CTCAE v. 4.03 Grade > 1) however,
             alopecia, sensory neuropathy Grade less than or equal to 2, or other Grade less than
             or equal to 2 not constituting a safety risk based on investigator s judgment are
             acceptable.

          -  Pregnancy or lactation period. Note: a negative pregnancy test is required for women
             of childbearing potential. Women who are postmenopausal (age-related amenorrhea
             greater than or equal to 12 consecutive months or follicle-stimulating hormone (FSH) >
             40 milli international units per milliliter [mIU/ml]), or who had undergone
             hysterectomy or bilateral oophorectomy are exempt from pregnancy testing. If necessary
             to confirm postmenopausal status a FSH level will be included at screening.

          -  Pregnant women are excluded from this study because Avelumab is in the class of agents
             known as antineoplastics/monoclonal antibodies with the potential for teratogenic or
             abortifacient effects. Because there is an unknown but potential risk for adverse
             events in

        nursing infants secondary to treatment of the mother with Avelumab, breastfeeding should be
        discontinued if the mother is treated with Avelumab.

          -  Known alcohol or drug abuse.

          -  Clinically significant (i.e. active) cardiovascular disease: cerebral vascular
             accident/stroke (< 6 months prior to enrollment), myocardial infarction (< 6 months
             prior to enrollment), unstable angina, congestive heart failure greater than or equal
             to New York Heart Association Classification Class II, or serious cardiac arrhythmia
             requiring medication.

          -  All other severe acute or chronic medical conditions including immune colitis,
             inflammatory bowel disease, immune pneumonitis, pulmonary fibrosis or psychiatric
             conditions including recent (within the past year) or active suicidal ideation or
             behavior; or laboratory abnormalities that may increase the risk associated with study
             participation or study treatment administration or may interfere with the
             interpretation of study results and, in the judgment of the investigator, would make
             the participants inappropriate for entry into this study.

          -  Any psychiatric condition that would prohibit the understanding or rendering of
             informed consent.

          -  Legal incapacity or limited legal capacity.

          -  Non-oncology vaccine therapies for prevention of infection disease (e.g. seasonal flu
             vaccine, human papilloma virus vaccine) within 4 weeks of study drug administration
             with the exception of vaccinations against COVID-19. Vaccination while on study is
             also prohibited except for administration of inactivated vaccines (e.g. inactivated
             influenza vaccines) and vaccinations against COVID-19.

          -  HIV-positive TET participants are ineligible because of the risk of developing
             opportunistic infections after treatment with an immune checkpoint inhibitor. Prior
             cases of disseminated herpes virus and fungal infections have been documented in this
             patient population.