Marine microbes, including viruses, are an essential part of the marine ecosystem, forming the base of the food web and driving biogeochemical cycles. Within this system, the composition of viral assemblages changes markedly with time, and some of these changes are repeatable through time; however, the extent to which these dynamics are reflected within versus among evolutionarily related groups of viruses is largely unexplored. To examine these dynamics, changes in the composition of two groups of ecologically important viruses and communities of their potential hosts were sampled every 2 weeks for 13-months at a coastal site in British Columbia, Canada. We sequenced two marker genes for viruses—the gene encoding the major capsid protein of T4-like phages and their relatives (gp23) and the RNA-dependent RNA polymerase (RdRp) gene of marnavirus-like RNA viruses—as well as marker genes for their bacterial and eukaryotic host communities, the genes encoding 16S rRNA and 18S rRNA. There were strong lagged correlations between viral diversity and community similarity of putative hosts, implying that the viruses influenced the composition of the host communities. The results showed that for both viral assemblages, the dominant clusters of phylogenetically related viruses shifted over time, and this was correlated with environmental changes. Viral clusters contained many ephemeral taxa and few persistent taxa, but within a viral assemblage, the ephemeral and persistent taxa were closely related, implying ecological dynamics within these clusters. Furthermore, these dynamics occurred in both the RNA and DNA viral assemblages surveyed, implying that this structure is common in natural viral assemblages.