To evaluate safety and response rate of durvalumab/tremelimumab in combination with paclitaxel in patients with metastatic gastric cancers who fail a first-line chemotherapy

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.