Telomerase adds G-rich telomeric repeats to the 3' ends of telomeres1, counteracting telomere shortening caused by loss of telomeric 3' overhangs during leading-strand DNA synthesis ("the end-replication problem"2). We report a second end-replication problem that originates from the incomplete duplication of the C-rich telomeric repeat strand by lagging-strand synthesis. This problem is solved by CST-Polymeraseα(Polα)-primase fill-in synthesis. In vitro, priming for lagging-strand DNA replication does not occur on the 3' overhang and lagging-strand synthesis stops in an ~150-nt zone more than 26 nt from the end of the template. Consistent with the in vitro data, lagging-end telomeres of cells lacking CST-Polα-primase lost ~50-60 nt of CCCTAA repeats per population doubling (PD). The C-strands of leading-end telomeres shortened by ~100 nt/PD, reflecting the generation of 3' overhangs through resection. The measured overall C-strand shortening in absence of CST-Polα-primase fill-in is consistent with the combined effects of incomplete lagging-strand synthesis and 5' resection at the leading-ends. We conclude that canonical DNA replication creates two telomere end-replication problems that require telomerase to maintain the G-strand and CST-Polα-primase to maintain the C-strand.