Asciminib Roll-over Study

Key Inclusion Criteria: 1. Participant with PH+ CML or PH+ ALL currently receiving treatment with asciminib (single agent or in combination with imatinib, nilotinib or dasatinib), imatinib, nilotinib or bosutinib alone within a Novartis-sponsored study and, in the opinion of the Investigator, would benefit from continued treatment. 2. Participant has demonstrated compliance on the parent study protocol and is willing and able to comply with scheduled visits, treatment plans and any other study procedures. Key Exclusion Criteria: 1. Participant has been discontinued from parent study treatment. 2. Participant currently has unresolved toxicities reported as possibly related to study treatment in the parent study. 3. Participant's ongoing treatment is currently approved and reimbursed at country level. 4. Pregnant or nursing (lactating) women. 5. Women of child-bearing potential, unless they are using highly effective methods of contraception and willing to continue while taking study treatment. 6. Sexually active males receiving imatinib, nilotinib, bosutinib or dasatinib unwilling to follow the relevant contraception requirements in the local prescribing information. 7. Applicable for participants on bosutinib treatment at the end of the CABL001A2301 and on other TKIs for CABL001A2202 study that switch to asciminib treatment: * Asymptomatic (grade 2) pancreatitis if not resolved within 28 days * QTcF\>480msec or inability to determine QTc interval * any grade 3 or 4 toxicity not resolved to grade 2 or lower within 28 days before starting asciminib treatment Other protocol-defined Inclusion/Exclusion criteria may apply.