Purpose: Stopping imatinib in patients with chronic myeloid leukemia in complete molecular remission during two following years. The objectives of this study are to determine the rate of patients without a molecular relapse and so the rate of molecular relapse, to determine and to seek for clinical and biological CML-related factors predictive for a molecular relapse after imatinib discontinuation. These objectives require to increase the number of study patients to be enrolled for accurate statistical considerations. It will allow to predict which patients have to be proposed for discontinuation without risk of molecular relapse and to select the patients who need to continue or reinforce the treatment to achieve a complete long term eradication of the disease.