The Executive Committee of the International Committee on Taxonomy of Viruses (ICTV) recognizes the need for a standardized nomenclature for virus species. This article sets out the case for establishing a binomial nomenclature and presents the advantages and disadvantages of different naming formats. The Executive Committee understands that adopting a binomial system would have major practical consequences, and invites comments from the virology community before making any decisions to change the existing nomenclature. The Executive Committee will take account of these comments in deciding whether to approve a standardized binomial system at its next meeting in October 2020. Note that this system would relate only to the formal names of virus species and not to the names of viruses.