Philosophiae Doctor - PhD / The plasticity of single-stranded viral genomes permits the formation of secondary structures through complementary base-pairing of their component nucleotides. Such structures have been shown to regulate a number of biological processes during the viral life-cycle including, replication, translation, transcription, post-transcriptional editing and genome packaging. However, even randomly generated single-stranded nucleotide sequences have the capacity to form stable secondary structures and therefore, amongst the numerous secondary structures formed in large viral genomes only a few of these elements will likely be biologically relevant. While it is possible to identify functional elements through series of laboratory experiments, this is both excessively resource- and time-intensive, and therefore not always feasible. A more efficient approach involves the use of computational comparative analyses methods to study the signals of molecular evolution that are consistent with selection acting to preserve particular structural elements. In this study, I systematically deploy a collection of computationally-based molecular evolution detection methods to analyse the genomes of viruses belonging to a number of ssRNA viral families (Alphaflexiviridae, Arteriviridae, Caliciviridae, Closteroviridae, Coronavirinae, Flaviviridae, Luteoviridae, Picornaviridae, Potyviridae, Togaviridae and Virgaviridae), for evidence of selectively stabilised secondary structures. To identify potentially important structural elements the approach incorporates structure prediction data with signals of natural selection, sequence co-evolution and genetic recombination. In addition, auxiliary computational tools were used to; 1) quantitatively rank the identified structures in order of their likely biological importance, 2) plot co-ordinates of structures onto viral genome maps, and 3) visualise individual structures, overlaid with estimates from the molecular evolution analyses. I show that in many of these viruses purifying selection tends to be stronger at sites that are predicted to be base-paired within secondary structures, in addition to strong associations between base-paired sites and those that are complementarily co-evolving. Lastly, I show that in recombinant genomes breakpoint locations are weakly associated with co-ordinates of secondary structures. Collectively, these findings suggest that natural selection acting to maintain potentially functional secondary structures has been a major theme during the evolution of these ssRNA viruses.