Tandem repeats are ubiquitous in nature and constitute a major source of genetic variability in populations. This variability is associated with a number of genetic disorders in humans including triplet expansion diseases such as Fragile X syndrome and Huntington's disease. The mechanism responsible for the variability/instability of these tandem arrays remains contentious. We show here that formation of secondary structures, in particular intrastrand tetraplexes, is an intrinsic property of some of the more unstable arrays. Tetraplexes block DNA polymerase progression and may promote instability of tandem arrays by increasing the likelihood of reiterative strand slippage. In the course of doing this work we have shown that some of these tetraplexes involve unusual base interactions. These interactions not only generate tetraplexes with novel properties but also lead us to conclude that the number of sequences that can form stable tetraplexes might be much larger than previously thought.