Viruses of four families of arthropod-specific, large dsDNA viruses (the nuclear arthropod large DNA viruses, or NALDVs) possess homologs of genes encoding conserved components involved in the baculovirus primary infection mechanism. The presence of such homologs encodingper osinfectivity factors (pifgenes), along with their absence from other viruses and the occurrence of other shared characteristics, suggests a common origin for the viruses of these families. Therefore, the classNaldaviriceteswas recently established, accommodating these four families. In addition, within this class, the ICTV approved the creation of the orderLefaviralesfor three of these families, whose members carry homologs of the baculovirus genes that code for components of the viral RNA polymerase, which is responsible for late gene expression. We further established a system for the binomial naming of all virus species in the orderLefavirales, in accordance with a decision by the ICTV in 2019 to move towards a standardized nomenclature for all virus species. The binomial species names for members of the orderLefaviralesconsist of the name of the genus to which the species belongs (e.g.,Alphabaculovirus), followed by a single epithet that refers to the host species from which the virus was originally isolated. The common names of viruses and the abbreviations thereof will not change, as the format of virus names lies outside the remit of the ICTV.Supplementary InformationThe online version contains supplementary material available at 10.1007/s00705-023-05793-8.