Some cancers utilize the recombination-dependent process of alternative lengthening of telomeres (ALT) to maintain long heterogeneous telomeres. Here, we studied the recombinational telomere elongation (RTE) of the Kluyveromyces lactis stn1-M1 mutant. We found that the total amount of the abundant telomeric DNA in stn1-M1 cells is subject to rapid variation and that it is likely to be primarily extrachromosomal. Rad50 and Rad51, known to be required for different RTE pathways in Saccharomyces cerevisiae, were not essential for the production of either long telomeres or telomeric circles in stn1-M1 cells. Circles of DNA containing telomeric repeats (t-circles) either present at the point of establishment of long telomeres or introduced later into stn1-M1 cells each led to the formation of long tandem arrays of the t-circle's sequence, which were incorporated at multiple telomeres. These tandem arrays were extraordinarily unstable and showed evidence of repeated rounds of concerted amplification. Our results suggest that the maintenance of telomeres in the stn1-M1 mutant involves extreme turnover of telomeric sequences from processes including both large deletions and the copying of t-circles.