Sequences were recently obtained from four double-stranded (ds) RNAs from different plant species. These dsRNAs are not associated with particles and as they appeared not to be horizontally transmitted, they were thought to be a kind of RNA plasmid. Here we report that the RNA-dependent RNA polymerase (RdRp) and helicase domains encoded by these dsRNAs are related to those of viruses of the alpha-like virus supergroup. Recent work on the RdRp sequences of alpha-like viruses raised doubts about their relatedness, but our analyses confirm that almost all the viruses previously assigned to the supergroup are related. Alpha-like viruses have single-stranded (ss) RNA genomes and produce particles, and they are much more diverse than the dsRNAs. This difference in diversity suggests the ssRNA alpha-like virus form is older, and we speculate that the transformation to a dsRNA form began when an ancestral ssRNA virus lost its virion protein gene. The phylogeny of the dsRNAs indicates this transformation was not recent and features of the dsRNA genome structure and translation strategy suggest it is now irreversible. Our analyses also show some dsRNAs from distantly related plants are closely related, indicating they have not strictly co-speciated with their hosts. In view of the affinities of the dsRNAs, we believe they should be classified as viruses and we suggest they be recognized as members of a new virus genus (Endornavirus) and family (Endoviridae).