Prolymphocytic leukemia T is a rare disease representing approximately 2% of mature lymphoid leukemias and 20% of prolymphocytic leukemias. It mainly affects the elderly with an aggressive clinical course. It is a hemopathy exhibiting a post thymic T phenotype (Tdt-, CD1a-, CD5 +, CD2 + and CD7 +), generally CD4 + / CD8-, but also CD4 + / CD8 + or CD8 + / CD4-. The main feature of T-PLL is the rearrangement of chromosome 14 involving genes encoding the T cell receptor complex (TCR) subunits, leading to overexpression of the proto-oncogene TCL1. On the molecular level, the study of Prolymphocytic leukemia T shows a substantial mutational activation of the IL2RG-JAK1-JAK3-STAT5B axis. Patients with Prolymphocytic leukemia T have a poor prognosis, due to a poor response to conventional chemotherapy. Treatment with the anti-CD52 monoclonal antibody: alemtuzumab has considerably improved the results, but the responses to treatment are transient; therefore, patients who obtain a response to alemtuzumab treatment are candidates for stem cell allograft (TSS) if they are eligible for this procedure. This combined approach extended the median survival to four years or more. However, new approaches using well-tolerated therapies that target signaling and survival pathways are necessary for most patients who are unable to receive intensive chemotherapy, such as JAK STAT axis inhibitors, anti-AKT, or anti BCL2 . Main objective: Better manage prolymphocytic T leukemias. Secondary objectives: * Molecular characterization of prolymphocytic leukemia T. * Study of the response to treatment, disease-free survival, overall survival. * Impact of prognostic factors on response to treatment, and survival.