Inclusion Criteria:

          1. Aged at least 18 years old (≥ 20 if in Japan), be able to provide a signed and dated,
             written informed consent.

          2. With documented histological or cytological confirmed locally advanced or metastatic
             NSCLC with EGFR or HER2 mutations.

          3. (ECOG) performance status 0-1.

          4. Predicted life expectancy ≥ 12 weeks

          5. Patient must have measurable disease according to RECIST 1.1.

          6. Patients with brain metastasis (BM) can be enrolled under the condition that BM is
             stable, neurologically asymptomatic and does not require corticosteroid treatment.

          7. Adequate organ system function.

        Exclusion Criteria:

          1. For part B: Patients who have received prior treatment with Poziotinib or TAK788 or
             other EGFR/HER2 exon20 insertion inhibitors should be excluded. Prior treatment with
             currently approved EGFR TKIs for sensitizing or T790M resistance mutations, such as
             gefitinib, erlotinib, osimertinib, afatinib and dacomitinb, are allowed.

          2. Treatment with EGFR or HER2 antibodies, major surgery (excluding placement of vascular
             access), or onco-immunotherapy (e.g. immune checkpoint inhibitors PD-1, PD-L1, CTLA-4)
             within 4 weeks before screening.

          3. Any cytotoxic chemotherapy, investigational agents or other anticancer drugs from a
             previous treatment regimen or clinical study within 14 days before screening.

          4. Radiotherapy with a limited field of radiation for palliation within 1 week of the
             first dose or with a wide field of radiation which must be completed within 4 weeks
             before screening.

          5. Receiving (or unable to stop using) medications or herbal supplements known to be
             potent inhibitors or inducers of CYP3A within 2-3 weeks before screening.

          6. Grapefruit, grapefruit juice, and orange marmalade (made with Seville oranges) within
             1 week before screening.

          7. Any unresolved toxicities from prior therapy greater than CTCAE grade 1 at the time of
             starting DZD9008 with the exception of alopecia and grade 2 prior platinum-therapy
             related neuropathy.

          8. Spinal cord compression or leptomeningeal metastasis.

          9. As judged by the investigator, any evidence of severe or uncontrolled systemic
             diseases, which would jeopardize compliance with the protocol, or active infection
             including hepatitis B, hepatitis C and human immunodeficiency virus (HIV).

         10. Any of the following cardiac criteria: (1) Mean resting corrected QT interval (QTcF) >
             470 msec obtained from 3 electrocardiograms (ECGs); (2) Any clinically significant
             abnormalities in rhythm, conduction or morphology of resting ECG, e.g., complete left
             bundle branch block, third degree heart block, and second-degree heart block, PR
             interval > 250 msec. (3) Any factors that increase the risk of QTcF prolongation, such
             as heart failure, hypokalemia, congenital long QT syndrome, family history of long QT
             syndrome or unexplained sudden death under 40 years of age in first degree relatives
             or any concomitant medication known to prolong the QT interval

         11. Past medical history of interstitial lung disease, drug-induced interstitial lung
             disease, radiation pneumonitis which required steroid treatment, or any evidence of
             clinically active interstitial lung disease

         12. Refractory nausea and vomiting, chronic gastrointestinal diseases, inability to
             swallow the formulated product or previous significant bowel resection that would
             preclude adequate absorption of DZD9008

         13. History of hypersensitivity to active or inactive excipients of DZD9008 or drugs with
             a similar chemical structure or class to DZD9008

         14. Women who are pregnant or breast feeding

         15. Involvement in the planning and conduct of the study.

         16. Judgment by the investigator that the patient should not participate in the study if
             the patient is unlikely to comply with study procedures, restrictions and
             requirements.