Telomeres, nucleoprotein complexes protecting the ends of linear chromosomes, are essential for ensuring the stability of eukaryotic genomes. As telomeres generally consist of repetitive DNA associated with specifically bound proteins, the evolution of telomeric repeat motifs hardly occurs. However, a recent study identified nematodes with telomeric repeats other than the canonical TTAGGC motif. Here, we investigated how telomere repeats were able to evolve despite the challenge posed by the specificity of telomere-binding proteins to the telomeric DNA in Nematoda, focusing on CEH-37. Initially, we assessed the conservation of telomere-binding proteins across diverse nematode species and obtained the well-conserved telomere-binding protein CEH-37 from each species with different telomeric repeats. The binding affinities of the proteins, measured by electrophoresis mobility shift assays, revealed that CEH-37 exhibits limited specificity, which cannot distinguish telomeric repeats found in nematodes except for TTAGGG motif. Furthermore, through the analysis of TBP conservation and the structure of CEH-37 in nematodes, we inferred that CEH-37 functioned as a double-stranded telomeric DNA binding protein before TEBP proteins emerged. Through this study, we suggest that telomeric sequences in Nematoda were able to evolve within the range of that does not exceed the sequence-specificity of telomere-binding proteins.