Telomeres, the ends of eukaryotic chromosomes, have long been recognized as specialized structures. Their stability compared with broken ends of chromosomes suggested that they have properties which protect them from fusion, degradation or recombination. Furthermore, a linear DNA molecule such as that of a eukaryotic chromosome must have a structure at its ends which allows its complete replication, as no known DNA polymerase can initiate synthesis without a primer. At the ends of the relatively short, multi-copy linear DNA molecules found naturally in the nuclei of several lower eukaryotes, there are simple tandemly repeated sequences with, in the cases analysed, a specific array of single-strand breaks, on both DNA strands, in the distal portion of the block of repeats. In general, however, direct analysis of chromosomal termini presents problems because of their very low abundance in nuclei. To circumvent this problem, we have previously cloned a chromosomal telomere of the yeast Saccharomyces cerevisiae on a linear DNA vector molecule. Here we show that yeast chromosomal telomeres terminate in a DNA sequence consisting of tandem irregular repeats of the general form C1-3A. The same repeat units are added to the ends of Tetrahymena telomeres, in an apparently non-template-directed manner, during their replication on linear plasmids in yeast. Such DNA addition may have a fundamental role in telomere replication.