Bosutinib is a potent tyrosine kinase inhibitor (TKI) active at nM concentration on BCR-ABL1 and most BCR-ABL1 mutations. Bosutinib has been approved by the FDA and the EMA for the treatment of patients with Ph+/BCR-ABL1+ chronic myeloid leukemia who fail treatment with other TKIs, first or second line. The goal of second-line treatment of CML is to achieve a response that would predict for a survival equal to, or very close to, the survival of non leukemic people, that is to say to achieve a complete cytogenetic response (CCyR) or a major molecular response (MMR). To achieve that goal, it is necessary to find and keep the right balance between activity, safety, and tolerability. There are no studies comparing TKIs in second-line. From phase 2, single-arm, studies, the reported efficacy of Bosutinib is similar to the reported efficacy of dasatinib and nilotinib. The median age of newly diagnosed CML patients is about 56 years, and at least 40% of all newly diagnosed patients are more than 60 years old. Particularly for these patients, the choice of the TKI must take into account the safety and the tolerability profile of the TKIs. The use of dasatinib and nilotinib is burdened by pleural and pulmonary complications, by infections, and by cardiovascular, thrombotic and metabolic (diabetes mellitus, dyslipidemia) complications. These complications are more frequent and more clinically relevant in the elderly. The safety and tolerability of Bosutinib has been reported in first- as well as in second- and third-line. The standard dose (500 mg once daily) is tolerated and safe, but at that dose several adverse events (AEs) limit the tolerability, require dose reduction or interruption, and affect patient quality of life, including diarrhea, nausea, vomiting, skin rash. Also an increase of AST, ALT and lipase are of concern and a cause of treatment discontinuation. On the contrary, an increased frequency of infections and of pleuro-pulmonary, cardiovascular, thrombotic, and metabolic AEs has not been reported. The reported hematologic toxicity of Bosutinib is at least as low as, or even lower than, that reported for the other TKIs, in spite of the fact that Bosutinib is a dual, BCR-ABL1 and src inhibitor. Until today, all studies of TKIs in CML have tested a fixed initial dose, providing for dose adjustment in case of toxicity (dose decrease) or in case of unsatisfactory response (dose increase). No study so far was designed to test the adaptation of the dose to the response, taking advantage of the fact that the efficacy of TKI treatment can be assessed rapidly and precisely by measuring the BCR-ABL1 transcripts level with real-time PCR (RT-PCR) in peripheral blood cells. An RT-PCR monthly for the first few months provides the best assessment of the response to treatment. We predict that a more flexible strategy of treatment (adapting the dose to the response) will result into a more convenient balance between activity and toxicity, hence into a better outcome. Based on these premises, it is proposed to test the activity, the safety, and the tolerability of Bosutinib, second-line, beginning with a low dose and adjusting subsequent doses based on molecular response, and on AEs, in a population of elderly patients. In almost all prior studies of TKIs in second- or third-line, the primary efficacy was assessed using cytogenetic response, both major and complete, at different time points. To make the results of this study comparable to the results of prior studies, the cytogenetic response will be evaluated as specified in section 5, but since the response to therapy and the evaluation of the efficacy of therapy are more and more based on molecular response, dose adaptation and efficacy evaluation will be based primarily on molecular response.