Chromosomal translocations that fuse the ABL1 gene to BCR and TEL cause human leukemias. Oligomerization and the loss of an inhibitory myristoylation modification lead to unregulated kinase activity of the BCR-ABL and TEL-ABL fusion proteins. ATP-competitive ABL inhibitors, such as imatinib and ponatinib, are effective against both fusion proteins. We discovered that asciminib, an allosteric inhibitor of BCR-ABL that binds to the myristoyl binding site in the ABL kinase domain, is 2000-fold less potent against TEL-ABL than BCR-ABL in cell-growth assays. This is surprising because the ABL components of the two fusion proteins, including the asciminib binding sites, have identical sequence. We deleted a short helical segment in the ABL kinase domain that closes over asciminib when it is bound. This deletion results in asciminib resistance in BCR-ABL, but has no effect on TEL-ABL, suggesting that the native autoinhibitory mechanism that asciminib engages in BCR-ABL is disrupted in TEL-ABL. We show, using mammalian cell expression and single-molecule microscopy, that BCR-ABL is mainly dimeric while TEL-ABL forms higher-order oligomers. Oligomerization can promote trans-autophosphorylation of ABL, and we find that a regulatory phosphorylation site in the SH3 domain of ABL (Tyr 89) is highly phosphorylated in TEL-ABL. This phosphorylation is expected to disassemble the autoinhibited conformation of ABL, thereby preventing asciminib binding. We show that TEL-ABL is intrinsically susceptible to inhibition by asciminib, but that increased phosphorylation results in resistance. Our results demonstrate that different ABL fusion proteins can have dramatically different responses to allosteric inhibitors due to differential phosphorylation.