Asgardarchaeota harbour many eukaryotic signature proteins and are widely considered to represent the closest archaeal relatives of eukaryotes. Whether similarities between Asgard archaea and eukaryotes extend to their viromes remains unknown. Here we present 20 metagenome-assembled genomes of Asgardarchaeota from deep-sea sediments of the basin off the Shimokita Peninsula, Japan. By combining a CRISPR spacer search of metagenomic sequences with phylogenomic analysis, we identify three family-level groups of viruses associated with Asgard archaea. The first group, verdandiviruses, includes tailed viruses of the class Caudoviricetes (realm Duplodnaviria); the second, skuldviruses, consists of viruses with predicted icosahedral capsids of the realm Varidnaviria; and the third group, wyrdviruses, is related to spindle-shaped viruses previously identified in other archaea. More than 90% of the proteins encoded by these viruses of Asgard archaea show no sequence similarity to proteins encoded by other known viruses. Nevertheless, all three proposed families consist of viruses typical of prokaryotes, providing no indication of specific evolutionary relationships between viruses infecting Asgard archaea and eukaryotes. Verdandiviruses and skuldviruses are likely to be lytic, whereas wyrdviruses potentially establish chronic infection and are released without host cell lysis. All three groups of viruses are predicted to play important roles in controlling Asgard archaea populations in deep-sea ecosystems.