This is a Phase 1/2, open-label, multicenter study in Japanese patients with locally advanced or metastatic NSCLC. This study will be conducted in two parts. Phase 1 is designed to observe the maximum tolerated dose (MTD) or maximum administered dose (MAD) of poziotinib when administered once daily or twice daily. Phase 2 will evaluate the safety and efficacy of the dose determined in Phase 1. Study participation includes a 30 day screening period, up to 24 months of treatment, and long-term follow-up for a maximum of 24 months after discontinuation of study treatment.

Phase 1 will enroll up to 36 patients into a dose finding study with two parallel, randomized dose groups. Each group will undergo a dose-finding scheme using a 3+3 design with the assessment of dose-limiting toxicities (DLTs) at up to three dose levels. Patients will be randomized into once daily (QD) or twice daily (BID) dose groups. The DLT assessment will be conducted in the first cycle of treatment and therefore, poziotinib dose modifications are not permitted during this cycle. Patients will be hospitalized for the first 2 weeks.

Phase 2 will enroll 40 additional NSCLC patients with EGFR (20 patients) or HER2 (20 patients) exon 20 insertion mutations. Efficacy and safety of the dose and dosing regimen determined in Phase 1 will be evaluated. All patients will be treated in 28-day cycles for up to 24 months.