Inclusion Criteria:

          -  Participants with histologically or cytologically confirmed stage IV NSCLC not
             amenable to curative surgery or radiation

          -  Participants may have had prior chemotherapy or be chemotherapy naïve

          -  Participants must have tumors that lack sensitizing EGFR mutation (e.g. exon 19
             deletion or exon 21 L858R) or ALK rearrangement. If a participant has squamous
             histology, then EGFR and ALK testing is not required.

          -  No prior treatment with cancer immunotherapy including, but not limited to, other
             anti-CTLA-4, anti-PD-1, anti-PD-L1, and anti-programmed cell death ligand 2 anti-
             (PD-L2) antibodies, excluding therapeutic anticancer vaccines.

          -  Participants will have 6 or less extracranial sites, which can safely receive SBRT
             between 30 - 50 Gy in 5 fractions. A site may have multiple tumor lesions within it as
             long as the gross tumor volume (GTV) of the site is 8 cm or less and can be covered in
             an acceptable SBRT field determined by the PI. All gross disease must be amenable to
             treatment with SBRT, as allowable per normal tissue constraints. Participants will not
             have had any prior radiation therapy significantly overlapping a tumor site to be
             treated.

          -  Participants must have evaluable disease, as defined by RECIST 1.1.

          -  World Health Organization (WHO)/Eastern Cooperative Oncology Group (ECOG) performance
             status of 0 or 1 at enrollment

          -  Life expectancy of > 12 weeks

          -  Participant is willing and able to comply with the protocol for the duration of the
             study including undergoing treatment and scheduled visits and examinations including
             follow up.

          -  Participants with treated metastatic lesions to the brain may be enrolled after
             completing stereotactic radiosurgery (may enroll 14 days after treatment) or whole
             brain radiation (may enroll 14 days after treatment) and must be off corticosteroids
             for 14 days prior to start of SBRT.

          -  Adequate normal organ and marrow function as defined below:

               -  Hemoglobin ≥ 9.0 g/dL

               -  Absolute neutrophil count (ANC) ≥ 1.5 x 10^9/L (> 1500 per mm^3)

               -  Platelet count ≥ 100 x 10^9/L (>100,000 per mm^3)

               -  Serum bilirubin ≤ 1.5 x institutional upper limit of normal (ULN). This will not
                  apply for participants with confirmed Gilbert's syndrome, who will be allowed in
                  consultation with their physician.

               -  AST (SGOT)/ALT (SGPT) ≤ 2.5 x ULN unless liver metastases are present, in which
                  case ALT and AST must be ≤ 5x ULN

               -  Serum creatinine <1.5 x upper limit of normal (ULN) OR creatinine clearance
                  (CrCl) ≥30 mL/min for participants with creatinine levels >1.5 × institutional
                  ULN

          -  Female participant of childbearing potential should have a negative urine or serum
             pregnancy prior to receiving the first study treatment. If the urine test is positive
             or cannot be confirmed as negative, a serum pregnancy test will be required

          -  Female participants of childbearing potential should be willing to use 1 method of
             highly effective birth control, 2 methods of effective birth control, be surgically
             sterile, or abstain from heterosexual activity for the course of the study through 180
             days after the last dose of study medication. Participants of childbearing potential
             are those who have not been surgically sterilized or have not been free from menses
             for > 1 year.

          -  Evidence of post-menopausal status or negative urinary or serum pregnancy test for
             female pre-menopausal patients. Women will be considered post-menopausal if they have
             been amenorrheic for 12 months without an alternative medical cause. The following
             age-specific requirements apply:

               -  Women < 50 years of age would be considered post-menopausal if they have been
                  amenorrheic for 12 months or more following cessation of exogenous hormonal
                  treatments and if they have luteinizing hormone and follicle- stimulating hormone
                  levels in the post-menopausal range for the institution or underwent surgical
                  sterilization (bilateral oophorectomy or hysterectomy).

               -  Women ≥ 50 years of age would be considered post-menopausal if they have been
                  amenorrheic for 12 months or more following cessation of all exogenous hormonal
                  treatments, had radiation-induced oophorectomy with last menses >1 year ago, had
                  chemotherapy-induced menopause with > 1 year interval since last menses, or
                  underwent surgical sterilization (bilateral oophorectomy or hysterectomy).

          -  Participant must be willing and able to provide written informed consent for the
             trial.

        Exclusion Criteria:

          -  Involvement in the planning and/or conduct of the study (applies to both AstraZeneca
             staff and/or staff at the study site)

          -  Previous enrollment in the present study

          -  Mixed small-cell lung cancer and sarcomatoid variant NSCLC histology

          -  Any concurrent chemotherapy, IP, biologic, or hormonal therapy for cancer treatment.
             Concurrent use of hormonal therapy for non-cancer-related conditions (eg, hormone
             replacement therapy) is acceptable.

          -  Major surgical procedure (as defined by the Investigator) within 14 days prior to the
             start of study treatment.

          -  Participants with untreated spinal cord compression. Participants with spinal cord
             compression may be enrolled if stable after completing surgery (may enroll 14 days
             after surgery) or radiation (may enroll 14 days after radiation) and must be off
             corticosteroids for at least 14 days prior to the start of SBRT.

          -  Participants with untreated brain metastasis. Participants with metastatic lesions to
             the brain may be enrolled after completing stereotactic radiosurgery or whole brain
             radiation (may enroll 14 days after radiation and must be off corticosteroids for at
             least 14 days prior to the start of SBRT.

          -  Any previous treatment with a PD1 or PD-L1 inhibitor, including durvalumab or an
             anti-CTLA4 inhibitor including tremelimumab

          -  Participants with a known targetable EGFR mutation or ALK rearrangement

          -  History of another primary malignancy except for:

               -  Malignancy treated with curative intent and with no known active disease ≥2 years

               -  Non-metastatic prostate adenocarcinoma, or treated superficial non-invasive
                  bladder cancer

               -  Adequately treated carcinoma in situ without evidence of disease (eg, cervical
                  cancer in situ)

               -  Adequately treated non-melanoma skin cancer or lentigo maligna without evidence
                  of disease

          -  Receipt of the last dose of anti-cancer therapy (chemotherapy, immunotherapy,
             endocrine therapy, targeted therapy, biologic therapy, tumor embolization, monoclonal
             antibodies, other investigational agent) ≤ 14 days of registration

          -  Mean QT interval corrected for heart rate using Fridericia's formula (QTcF) ≥470 ms.
             Abnormality must be confirmed on 3 ECGs.

          -  Current or prior use of immunosuppressive medication within 14 days before the first
             dose of durvalumab or tremelimumab

        The following are exceptions to this criterion:

          -  Intranasal, inhaled, topical steroids, or local steroid injections (eg,
             intra-articular injection).

          -  Systemic corticosteroids at physiologic doses not to exceed 10 mg/day of prednisone or
             its equivalent

          -  Steroids as premedication for hypersensitivity reactions (eg, CT scan premedication)

          -  Active or known autoimmune disease that has required immunosuppressive systemic
             treatment in past 2 years (ie, with use of disease modifying agents, corticosteroids,
             or immunosuppressive drugs). Replacement therapy (eg, thyroxine, insulin, or
             physiologic corticosteroid replacement therapy for adrenal or pituitary insufficiency)
             is not considered a form of systemic treatment and is allowed. The following are
             exceptions to this criterion:

               -  Participants with vitiligo or alopecia,

               -  Grave's disease,

               -  Hypothyroidism (eg, following Hashimoto syndrome),

               -  Psoriasis not requiring systemic treatment (within the past 2 years)

               -  Participants with celiac disease controlled by diet alone

                    -  History of active primary immunodeficiency

                    -  History of allogeneic organ transplant

                    -  Active infection, including tuberculosis (clinical evaluation), hepatitis B,
                       hepatitis C, or human immunodeficiency virus (HIV, positive HIV 1 or 2
                       antibodies). Active hepatitis B virus (HBV) is defined by a known positive
                       HBV surface antigen (HBsAg) result. Participants with a past or resolved HBV
                       infection (defined as the presence of hepatitis B core antibody and absence
                       of HBsAg) are eligible. Participants positive for hepatitis C virus (HCV)
                       antibody are eligible only if polymerase chain reaction is negative for HCV
                       ribonucleic acid (RNA).

                    -  History of leptomeningeal carcinomatosis

                    -  Receipt of live attenuated vaccination within 30 days prior to the first
                       dose of IP. Note: Participants, if enrolled, should not receive live vaccine
                       during the study and up to 30 days after the last dose of IP.

                    -  Any condition or uncontrolled intercurrent illness that, in the opinion of
                       the Investigator, would interfere with the evaluation of IP or
                       interpretation of patient safety or study results, including, but not
                       limited to, ongoing or active infection, symptomatic congestive heart
                       failure, uncontrolled hypertension, unstable angina pectoris, cardiac
                       arrhythmia, or psychiatric illness/social situations that would limit
                       compliance with study requirement, substantially increase risk of incurring
                       AEs from durvalumab or tremelimumab, or compromise the ability of the
                       patient to give written informed consent

                    -  Subjects with uncontrolled seizures.

                    -  Female participants who are pregnant or breast-feeding or male or female
                       patients of reproductive potential who are not willing to employ effective
                       birth control from screening to 180 days after the last dose of durvalumab
                       and tremelimumab combination therapy or 90 days after the last dose of
                       durvalumab monotherapy.

                    -  History of hypersensitivity to IP or comparator agents

                    -  History of medically diagnosed pneumonitis or interstitial lung disease