The B-DNA double helix can dynamically accommodate G-C and A-T base pairs in either Watson-Crick or Hoogsteen configurations. Here, we show that G-C(+) (in which + indicates protonation) and A-U Hoogsteen base pairs are strongly disfavored in A-RNA. As a result,N(1)-methyladenosine and N(1)-methylguanosine, which occur in DNA as a form of alkylation damage and in RNA as post-transcriptional modifications, have dramatically different consequences. Whereas they create G-C(+) and A-T Hoogsteen base pairs in duplex DNA, thereby maintaining the structural integrity of the double helix, they block base-pairing and induce local duplex melting in RNA. These observations provide a mechanism for disrupting RNA structure through post-transcriptional modifications. The different propensities to form Hoogsteen base pairs in B-DNA and A-RNA may help cells meet the opposing requirements of maintaining genome stability, on the one hand, and of dynamically modulating the structure of the epitranscriptome, on the other.