Retrotransposons can represent half of eukaryotic genomes. Retrotransposon dysregulation destabilizes genomes and has been linked to various human diseases. Emerging regulators of retromobility include RNA-DNA hybrid-containing structures known as R-loops. Accumulation of these structures at the transposons of yeast 1 (Ty1) elements has been shown to increase Ty1 retromobility through an unknown mechanism. Here, via a targeted genetic screen, we identified the rnh1Δ rad27Δ yeast mutant, which lacked both the Ty1 inhibitor Rad27 and the RNA-DNA hybrid suppressor Rnh1. The mutant exhibited elevated levels of Ty1 cDNA-associated RNA-DNA hybrids that promoted Ty1 mobility. Moreover, in this rnh1Δ rad27Δ mutant, but not in the double RNase H mutant rnh1Δ rnh201Δ, RNA-DNA hybrids preferentially existed as duplex nucleic acid structures and increased Ty1 mobility in a Rad52-dependent manner. The data indicate that in cells lacking RNA-DNA hybrid and Ty1 repressors, elevated levels of RNA-cDNA hybrids, which are associated with duplex nucleic acid structures, boost Ty1 mobility via a Rad52-dependent mechanism. In contrast, in cells lacking RNA-DNA hybrid repressors alone, elevated levels of RNA-cDNA hybrids, which are associated with triplex nucleic acid structures, boost Ty1 mobility via a Rad52-independent process. We propose that duplex and triplex RNA-DNA hybrids promote transposon mobility via Rad52-dependent or -independent mechanisms.