CRISPR-Cas systems provide bacteria with adaptive immunity against bacteriophages1. However, DNA modification2,3, the production of anti-CRISPR proteins4,5 and potentially other strategies enable phages to evade CRISPR-Cas. Here, we discovered a Serratia jumbo phage that evades type I CRISPR-Cas systems, but is sensitive to type III immunity. Jumbo phage infection resulted in a nucleus-like structure enclosed by a proteinaceous phage shell-a phenomenon only reported recently for distantly related Pseudomonas phages6,7. All three native CRISPR-Cas complexes in Serratia-type I-E, I-F and III-A-were spatially excluded from the phage nucleus and phage DNA was not targeted. However, the type III-A system still arrested jumbo phage infection by targeting phage RNA in the cytoplasm in a process requiring Cas7, Cas10 and an accessory nuclease. Type III, but not type I, systems frequently targeted nucleus-forming jumbo phages that were identified in global viral sequence datasets. The ability to recognize jumbo phage RNA and elicit immunity probably contributes to the presence of both RNA- and DNA-targeting CRISPR-Cas systems in many bacteria1,8. Together, our results support the model that jumbo phage nucleus-like compartments serve as a barrier to DNA-targeting, but not RNA-targeting, defences, and that this phenomenon is widespread among jumbo phages.