In the mammalian genome, certain genomic loci/regions pose greater challenges to the DNA replication machinery (i.e., the replisome) than others. Such known genomic loci/regions include centromeres, common fragile sites, subtelomeres, and telomeres. However, the detailed mechanism of how mammalian cells cope with the replication stress at these loci/regions is largely unknown. Here we show that depletion of FANCM, or of one of its obligatory binding partners, FAAP24, MHF1, and MHF2, induces replication stress primarily at the telomeres of cells that use the alternative lengthening of telomeres (ALT) pathway as their telomere maintenance mechanism. Using the telomere-specific single-molecule analysis of replicated DNA technique, we found that depletion of FANCM dramatically reduces the replication efficiency at ALT telomeres. We further show that FANCM, BRCA1, and BLM are actively recruited to the ALT telomeres that are experiencing replication stress and that the recruitment of BRCA1 and BLM to these damaged telomeres is interdependent and is regulated by both ATR and Chk1. Mechanistically, we demonstrated that, in FANCM-depleted ALT cells, BRCA1 and BLM help to resolve the telomeric replication stress by stimulating DNA end resection and homologous recombination (HR). Consistent with their roles in resolving the replication stress induced by FANCM deficiency, simultaneous depletion of BLM and FANCM, or of BRCA1 and FANCM, leads to increased micronuclei formation and synthetic lethality in ALT cells. We propose that these synthetic lethal interactions can be explored for targeting the ALT cancers.