Patients who have progressed after first-line treatment with afatinib as first tyrosine kinase inhibitor (TKI) will be screened while they are receiving second-line (induction) treatment consisting of cisplatin / carboplatin plus pemetrexed given in 21-day cycles. Patients who do not progress (i.e. complete or partial response, or stable disease - CR, PR or SD) after completion of at least three and not more than four chemotherapy cycles will be randomized (1:1 ratio) to receive maintenance therapy with either afatinib (40 mg/d or last tolerated dose during first-line treatment with afatinib as first TKI) or pemetrexed (500 mg/m2 or 375 mg/m2 if dose reduction was required every 21 days) until disease progression or treatment discontinuation because of patient decision or toxicity.