This is an open label, non-randomized, sequential, phase I/II trial in patients with stage IIIB or IV non-small cell lung cancer (NSCLC) with EGFR mutations after progression to Erlotinib. The study will have two parts. The first part (phase I) will be a dose finding (MTD) study to be implemented at three hospitals. The second part of the study (phase II) will asses the safety and efficacy of the combination. In this second part (phase II) patients will be treated with oral Erlotinib 150 mg P.O daily plus oral Vorinostat administered according to the results of the phase I. The study endpoints to be evaluated will include safety and response rate (RR) as primary endpoints and clinical benefit rate (CBR), time to progression, time to response, response duration and progression free survival as secondary endpoints. All the patients (phase I and II) will be treated until progression disease, unacceptable toxicity or withdrawal of the consent, and will be treated at the discretion of the principal investigator.