DNA repetitive sequences capable of adopting non-B DNA structures are a potent source of instability in eukaryotic genomes. They are strong inducers of chromosomal fragility and genome rearrangements that cause various hereditary diseases and cancers. In addition, a subset of repeats also has an ability to expand, which leads to more than 20 human genetic diseases that are collectively known as repeat expansion diseases. However, the mechanisms underlying the potential of these structure-prone motifs to break and expand are largely unknown. In this study, a systematic genome-wide screen was employed in yeast Saccharomyces cerevisiae to investigate the contributing factors of the instability of two representative non-B DNA-forming repeats: the triplex-adopting GAA/TTC tracts and the inverted repeats that can form hairpin and cruciform structures. The GAA/TTC screen revealed that DNA replication and transcription initiation are the two major pathways governing the GAA/TTC stability in yeast, as corresponding mutants strongly induce both fragility and large-scale expansions of the repeats. The inverted repeats screen and follow-up experiments revealed that both replication-dependent and -independent pathways are involved in maintaining the stability of palindromic sequences. We propose that similar mechanisms could operate in the human cells to mediate the deleterious metabolism of GAA and inverted repeats.