Inclusion Criteria:

          -  For inclusion in the study, patients should fulfill the following criteria

               -  Histological diagnosis of NSCLC; for non-squamous NSCLC: no known sensitizing
                  EGFR-mutation, no known EML4-ALK translocation. When a patient with non-squamous
                  NSCLC has a KRAS mutation, further testing for EGFR and EML4-ALK is not
                  necessary. For squamous NSCLC, EGFR and EML4-ALK testing is not necessary.

               -  Availability of adequate in quality and quantity archived tumor material for IHC
                  PD-L1 testing; (Preferably 15 but 8 mandatory slides or block of tumor tissue
                  will be collected);

               -  Stage IIIB or IIIC not eligible for radical treatment or stage IV according to
                  TNM8 (Ref. 6);

               -  Brain metastases should be treated with local therapy (stereotactic radiotherapy
                  or whole brain radiotherapy), and patients should be asymptomatic, without
                  treatment with steroids for four weeks before enrollment. Before enrollment, new
                  brain imaging (contrast-CT or gadolinium-MRI) is needed to demonstrate that there
                  is no progression in the brain when the last brain imaging is more than four
                  weeks earlier. Screening for brain metastases is not necessary in patients that
                  were previously not diagnosed with brain metastases and that are without signs
                  indicative of brain metastases.

               -  ≥ 18 years of age at time of study entry;

               -  WHO performance status 0 or 1; at enrollment

               -  Body weight > 30 kg at enrollment

               -  Evaluable disease with CT or MRI according to RECIST 1.1 (except for patients
                  with a CR after 4 cycles of platinum-based doublet chemotherapy, these patients
                  are also eligible);

               -  Stable disease or response by RECIST criteria response after 4 cycles of
                  platinum-based doublet chemotherapy;

               -  Adequate normal organ and marrow function:

               -  Absolute neutrophil count (ANC) ≥ 1.5 x 109/L (> 1500 per mm3)

               -  Platelet count ≥ 100 x 109/L (>100,000 per mm3)

               -  Serum bilirubin ≤ 1.5 x institutional upper limit of normal (ULN). This will not
                  apply to subjects with confirmed Gilbert's syndrome (persistent or recurrent
                  hyperbilirubinemia that is predominantly unconjugated in the absence of hemolysis
                  or hepatic pathology)AST (SGOT)/ALT (SGPT) ≤ 2.5 x institutional upper limit of
                  normal; for patients with liver metastases ≤ 5 x institutional upper limit of
                  normal

               -  Measured or calculated creatinine clearance ≥45 mL/min by the Cockcroft-Gault
                  formula (Appendix E)

               -  Haemoglobin ≥ 9.0 g/dL

               -  Patient with following autoimmune or inflammatory disorders are eligible:

               -  Vitiligo or alopecia

               -  Hypothyroidism (eg, following Hashimoto syndrome) stable on hormone replacement

               -  Any chronic skin condition that does not require systemic therapy

               -  Active disease in the last 5 years may be included but only after consultation
                  with the study investigator

               -  Celiac disease controlled by diet alone

               -  Patient with history of another primary malignancy are eligible in the following
                  cases:

               -  Malignancy treated with curative intent and with no known active disease ≥5 years
                  before the first dose of IP and of low potential risk for recurrence

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

               -  Adequately treated carcinoma in situ without evidence of disease

               -  Women of child bearing potential (WOCBP) must have a negative serum pregnancy
                  test within 72 hours prior to the first dose of study treatment.

        Note: women of childbearing potential are defined as premenopausal females capable of
        becoming pregnant (i.e. females who have had any evidence of menses in the past 12 months,
        with the exception of those who had prior hysterectomy). However, women who have been
        amenorrheic for 12 or more months are still considered to be of childbearing potential if
        the amenorrhea is possibly due to prior chemotherapy, antiestrogens, low body weight,
        ovarian suppression or other reasons.

          -  Patients of childbearing / reproductive potential should use adequate birth control
             measures, as defined by the investigator, during the study treatment period and from
             screening to 90 days after the last dose of durvalumab monotherapy or 180 days after
             the last dose of durvalumab + tremelimumab combination. A highly effective method of
             birth control is defined as a method which results in a low failure rate (i.e. less
             than 1% per year) when used consistently and correctly. Such methods include:

          -  Combined (estrogen and progestogen containing) hormonal contraception associated with
             inhibition of ovulation (oral, intravaginal, transdermal)

          -  Progestogen-only hormonal contraception associated with inhibition of ovulation (oral,
             injectable, implantable)

          -  Intrauterine device (IUD)

          -  Intrauterine hormone-releasing system (IUS)

          -  Bilateral tubal occlusion

          -  Vasectomized partner

          -  Sexual abstinence (the reliability of sexual abstinence needs to be evaluated in
             relation to the duration of the clinical trial and the preferred and usual lifestyle
             of the patient)

          -  Female subjects who are breast feeding should discontinue nursing prior to the first
             dose of study treatment, from screening to 90 days after the last dose of durvalumab
             monotherapy or 180 days after the last dose of durvalumab + tremelimumab combination
             therapy or pemetrexed.

          -  Subject 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;

          -  Before patient registration, written informed consent must be given according to
             ICH/GCP, and national/local regulations.

        Exclusion Criteria:

          -  Patients should not enter the study if any of the following exclusion criteria is
             fulfilled

               -  Concurrent enrollment in another clinical study, unless it is an observational
                  (non-interventional) clinical study or the follow-up period of an interventional
                  study

               -  Mixed small-cell lung cancer and NSCLC histology, sarcomatoid variant or large
                  cell neuro-endocrine variant

               -  Patients with known history of leptomeningeal carcinomatosis

               -  Any unresolved toxicity NCI CTCAE Grade ≥2 from previous anticancer therapy with
                  the exception of alopecia, vitiligo, and the laboratory values defined in the
                  inclusion criteria

               -  Patients with Grade ≥2 neuropathy will be evaluated on a case-by-case basis after
                  consultation with the study investigator

               -  Patients with irreversible toxicity not reasonably expected to be exacerbated by
                  treatment with durvalumab or tremelimumab may be included only after consultation
                  with the study investigator

               -  Any previous treatment with a PD1 or PD-L1 inhibitor, including durvalumab, a
                  CTLA-4 including tremelimumab or other checkpoint inhibitors or other immune
                  therapy during the last 12 months

               -  Current or prior use of immunosuppressive medication within 14 days before the
                  first dose of durvalumab and tremelimumab, with the exceptions of intranasal and
                  inhaled corticosteroids or systemic corticosteroids at physiological doses, which
                  are not to exceed 10 mg/day of prednisone, or an equivalent corticosteroid, or
                  steroids as premedication for hypersensitivity reactions (eg, CT scan
                  premedication)

               -  Radiotherapy treatment to more than 30% of the bone marrow or with a wide field
                  of radiation within 4 weeks of the first dose of study drug. Note: Local
                  treatment of isolated lesions, excluding target lesions, for palliative intent is
                  acceptable when it is not within 7 days of the first dose of study drug.

               -  Major surgical procedure (as defined by the study investigator) within 28 days
                  prior to the first dose of IP. Note: Local surgery of isolated lesions for
                  palliative intent is acceptable

               -  History of allogenic organ transplantation

               -  Receipt of live attenuated vaccination within 30 days prior to enrollement

               -  Active or prior documented autoimmune or inflammatory disorders (including
                  inflammatory bowel disease [eg, colitis or Crohn's disease], diverticulitis [with
                  the exception of diverticulosis], systemic lupus erythematosus, Sarcoidosis
                  syndrome, or Wegener syndrome [granulomatosis with polyangitis, Graves' disease,
                  rheumatoid arthritis, hypophysitis, uveitis, etc]).

               -  History of hypersensitivity to durvalumab, tremelimumab or any excipient

               -  Uncontrolled intercurrent illness including, but not limited to:

               -  Active infection including tuberculosis (clinical evaluation that includes
                  clinical history, physical examination and radiographic findings, and TB testing
                  in line with local practice), hepatitis B (known positive HBV surface antigen
                  (HBsAg) result), hepatitis C, or human immunodeficiency virus (positive HIV 1/2
                  antibodies). Patients with a past or resolved HBV infection (defined as the
                  presence of hepatitis B core antibody [anti-HBc] and absence of HBsAg) are
                  eligible. Patients positive for hepatitis C (HCV) antibody are eligible only if
                  polymerase chain reaction is negative for HCV RNA.

               -  Symptomatic congestive heart failure, uncontrolled hypertension (defined as blood
                  pressure above 160/90 mm Hg despite medication), unstable angina pectoris,
                  cardiac arrhythmia

               -  Active peptic ulcer disease or gastritis

               -  Liver cirrhosis CHILD B+, C (Appendix J)

               -  Active bleeding diatheses

               -  History of primary immunodeficiency

               -  Mean QT interval corrected for heart rate (QTc) ≥470 ms calculated from 3
                  electrocardiograms (ECGs) using Frediricia's Correction

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

               -  Any psychological, familial, sociological or geographical condition potentially
                  hampering compliance with the study protocol and follow-up schedule; those
                  conditions should be discussed with the patient before registration in the trial

               -  History of another primary malignancy

               -  For non-squamous: unable to interrupt aspirin or other nonsteroidal
                  anti-inflammatory agents, other than an aspirin dose <1.3 grams per day, for a
                  5-day period (8-day period for long-acting agents, such as piroxicam). Unable or
                  unwilling to take folic acid, vitamin B12 supplementation.