The invention provides antisense antiviral compounds and methods of their use and production in inhibition of growth of viruses of the Flaviviridae, Picornoviridae, Caliciviridae, Togaviridae, Arteriviridae, Coronaviridae, Astroviridae and Hepeviridae families in the treatment of a viral infection. The antisense antiviral compounds are substantially uncharged morpholino oligonucleotides having a sequence of 12-40 subunits, including at least 12 subunits having a targeting sequence that is complementary to a region associated with stem-loop secondary structure within the 5′-terminal end 40 bases of the positive-sense RNA strand of the virus.