Picornaviridae family includes several viruses of great economic and medical importance. Among all members of the family we focused our attention on the human rhinovirus, the most important etiologic agent of the common cold and on the foot-and-mouth disease virus that cause of an economically important disease in cattle. Despite the low sequence similarity of the polyprotein coding open reading frames of these highly divergent picornaviruses, they have in common structural and functional similarities including a similar genomic organization, a capsid structure composed of 60 copies of four different proteins, or 3D-structures showing similar general topology, among others. We hypothesized that such similarities could be reflected in emergent common compositional structures interspersed in their genomes which were not observed heretofore. Using a methodology categorizing nucleotide triplets by their gross-composition we have found two human rhinoviruses sharing compositional structures interspersed along their genomic RNA with three foot-and-mouth disease viruses. The shared compositional structures are in one case composed by nucleotide triplets containing all nearest-neighbours of A and G and in other case containing all nearest-neighbours of A, and C. The structures are under strong evolutionary constraints for variability, allowing the access to novel viral genomic motifs with likely biological relevance. The conserved fragments would be useful to predict critical mutation points sites important from the evolutionary point of view.