Carrier state viral infection constitutes an equilibrium state in which a limited fraction of a cellular population is infected while the remaining cells are transiently resistant to infection. This type of infection has been characterized for several bacteriophages but not, to date, for archaeal viruses. Here we demonstrate that the rudivirus SIRV3 can produce a host-dependent carrier state infection in the model crenarchaeon Sulfolobus. SIRV3 only infected a fraction of a Sulfolobus islandicus REY15A culture over several days during which host growth was unimpaired and no chromosomal DNA degradation was observed. CRISPR spacer acquisition from SIRV3 DNA was induced by coinfecting with the monocaudavirus SMV1 and it was coincident with increased transcript levels from subtype I-A adaptation and interference cas genes. However, this response did not significantly affect the carrier state infection of SIRV3 and both viruses were maintained in the culture over 12 days during which SIRV3 anti-CRISPR genes were shown to be expressed. Transcriptome and proteome analyses demonstrated that most SIRV3 genes were expressed at varying levels over time whereas SMV1 gene expression was generally low. The study yields insights into the basis for the stable infection of SIRV3 and the resistance to the different host CRISPR-Cas interference mechanisms. It also provides a rationale for the commonly observed coinfection of archaeal cells by different viruses in natural environments.