Inclusion Criteria:

          1. Written informed consent and any locally-required authorization obtained from the
             subject prior to performing any protocol-related procedures, including screening
             evaluations

          2. Age > 19 years at time of study entry or adult male or female (according to age of
             majority as defined as ≥ 19 years)

          3. Body weight > 30kg

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

          5. Life expectancy of > 12 weeks

          6. Adequate normal organ and marrow function as defined below; Hemoglobin ≥ 9.0 g/dL
             Absolute neutrophil count (ANC) ≥ 1.5 x 109/L (> 1,500 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 Gilbert's syndrome.

             AST (SGOT)/ALT (SGPT) ≤ 2.5 x institutional upper limit of normal unless liver
             metastases are present, in which case it must be ≤ 5x ULN Serum creatinine CL>40
             mL/min by the Cockcroft-Gault formula (Cockcroft and Gault 1976) or by 24-hour urine
             collection for determination of creatinine clearance

             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

          7. 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.

          8. (for the phase II section) Have one of the following targeted sequencing results 1)
             CD274 amplification 2) positive for mutations causing a hypermutation (PMS1, PMS2,
             MLH1, MLH3, MSH2, MSH3, MSH6, POLD1, POLD2, or POLE) 3) microsatellite instability
             (MSI high) 4) somatic exonic mutation rate-high 5) EBV positive

          9. (for the phase II section) Have at least one investigator-assessed measurable disease
             per RECIST v1.1

         10. Have a histologically- or cytologically-confirmed gastric carcinoma

         11. (for the phase II section) Have disease progression on or within 6 months of a
             first-line fluoropyrimidine/platinum-containing chemotherapy for metastatic disease or
             perioperative chemotherapy

        Exclusion Criteria:

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

          2. Previous enrollment in the present study

          3. Participation in another clinical study with an investigational product during the
             last 2 weeks

          4. (for the phase II section) Any previous treatment for metastatic disease with a PD1 or
             PD-L1, including durvalumab inhibitor or an anti-CTLA4 including tremelimumab, or with
             cancer vaccine, or with paclitaxel or docetaxel

          5. History of another primary malignancy except for Malignancy treated with curative
             intent and with no known active disease ≥ 5 years before the first dose of study drug
             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 eg, cervical cancer in situ

          6. Receipt of the last dose of anti-cancer therapy (chemotherapy, immunotherapy,
             endocrine therapy, targeted therapy including TKIs, tumor embolization, other
             investigational agent) ≤ 2 weeks prior to the first dose of study drug (≤ 4 weeks
             prior to the first dose of study drug for subjects who have received prior monoclonal
             antibodies or biologic therapy, and within 6 weeks for nitrosourea or mitomycin C).

          7. 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 Physician. 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 Physician

          8. Current or prior use of immunosuppressive medication within 14 days before the first
             dose of durvalumab or 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. Dexamethasone used
             for paclitaxel premedication is allowed.

          9. Any prior Grade ≥3 immune-related adverse event (irAE) while receiving any previous
             immunotherapy agent, or any unresolved irAE >Grade 1

         10. 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 polyangiitis, Graves' disease, rheumatoid
             arthritis, hypophysitis, uveitis, etc). The following are exceptions to this
             criterion: Patients with vitiligo or alopecia, Patients with hypothyroidism (eg,
             following Hashimoto syndrome) stable on hormone replacement, Any chronic skin
             condition that does not require systemic therapy, Patients without active disease in
             the last 5 years may be included but only after consultation with the study physician,
             Patients with celiac disease controlled by diet alone.

        11, History of primary immunodeficiency 12, History of allogeneic organ transplant 13.
        History of hypersensitivity to durvalumab or tremelimumab 14. History of anaphylaxis
        reactions to taxanes 15. Uncontrolled intercurrent illness including, but not limited to,
        ongoing or active, symptomatic congestive heart failure, uncontrolled hypertension,
        unstable angina pectoris, cardiac arrhythmia, active bleeding diatheses including any
        subject known to have evidence of acute or chronic active hepatitis B or hepatitis C, or
        psychiatric illness/social situations that would limit compliance with study requirements
        or compromise the ability of the subject to give written informed consent 16. Active
        infection including tuberculosis (clinical evaluation that includes clinical history,
        physical examination and radiographic findings), 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 17. History of leptomeningeal carcinomatosis 18. Receipt of live attenuated
        vaccination within 30 days prior to study entry or within 30 days of receiving durvalumab
        or tremelimumab 19. Female patients who are pregnant or breastfeeding 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 20. Any condition that, in
        the opinion of the investigator, would interfere with evaluation of study treatment or
        interpretation of patient safety or study results 21. Brain metastases or spinal cord
        compression unless the patient is stable (asymptomatic; no evidence of new or emerging
        brain metastases; and stable and off steroids and anti-convulsants for at least 14 days
        prior to start of study treatment.

        Patients with suspected brain metastases at screening should have an MRI (preferred) or CT
        each preferably with IV contrast of the brain prior to study entry; Following radiotherapy
        and/or surgery of the brain metastases patients must wait 4 weeks following the
        intervention and before treatment with imaging to confirm stability 22. Subjects with
        uncontrolled seizures. 23.Female patients who are pregnant or breastfeeding 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, tremelimumab
        combination therapy or 90 days after the last dose of durvalumab monotherapy, whichever is
        the longer time period 24.Known allergy or hypersensitivity to IP or any excipient If a
        patient withdraws from participation in the study, then his or her enrollment/randomization
        code cannot be reused.