Epidermal growth factor receptor tyrosine kinase inhibitors (EGFR-TKIs) are efficacious drugs for non-small cell lung cancers (NSCLCs) with EGFR-activating mutations. Afatinib, a second-generation EGFR-TKI and osimertinib, a third-generation EGFR-TKI, are both standard therapies for patients with these types of cancer. Each drug possesses distinct binding sites for the tyrosine kinase domain of EGFR. The present study examined the efficacy of single and combination TKI therapy using in vitro growth inhibition assays of Ba/F3 cells with an EGFR-activating Del19 mutation. Afatinib or osimertinib treatment alone markedly inhibited cell proliferation in Ba/F3 cells, although drug-resistant cells eventually appeared with secondary EGFR mutations (either T790M or C797S, respectively) as determined by direct sequencing. Notably a combination of afatinib and osimertinib eradicated Ba/F3 cells with no development of resistance. We also evaluated the efficacy of afatinib, osimertinib, and a combination of the two, using drug-resistant cells with T790M or C797S mutations. Osimertinib was effective for treating Ba/F3 cells with the T790M mutation, whereas afatinib was moderately effective against C797S Ba/F3 cells. However, subsequent treatment, even when both drugs were used in combination, could not completely eradicate the Ba/F3 population and doubly resistant cells with a variety of triple mutations were generated, including Del19/T790M/C797S. In conclusion, an initial treatment with a combination of osimertinib and afatinib is potentially more effective for eradicating mutant EGFR-dependent cells than sequential drug use. This should be tested in future clinical trials to establish whether such a combination would be effective for the treatment of NSCLC.