Borgs are huge, linear extrachromosomal elements associated with anaerobic methane-oxidizing archaea. Striking features of Borg genomes are pervasive tandem direct repeat (TR) regions. Here, we present six new Borg genomes and investigate the characteristics of TRs in all ten complete Borg genomes. We find that TR regions are rapidly evolving, recently formed, arise independently, and are virtually absent in host Methanoperedens genomes. Flanking partial repeats and A-enriched character constrain the TR formation mechanism. TRs can be in intergenic regions, where they might serve as regulatory RNAs, or in open reading frames (ORFs). TRs in ORFs are under very strong selective pressure, leading to perfect amino acid TRs (aaTRs) that are commonly intrinsically disordered regions. Proteins with aaTRs are often extracellular or membrane proteins, and functionally similar or homologous proteins often have aaTRs composed of the same amino acids. We propose that Borg aaTR-proteins functionally diversify Methanoperedens and all TRs are crucial for specific Borg-host associations and possibly cospeciation.