Many bacterial genomes carry prophages whose induction can eliminate competitors. In response, bacteria may become resistant by modifying surface receptors, by lysogenization, or by other poorly known processes. All these mechanisms affect bacterial fitness and population dynamics. To understand the evolution of phage resistance, we co-cultivated a phage-sensitive strain (BJ1) and a poly-lysogenic Klebsiella pneumoniae strain (ST14) under different phage pressures. The population yield remained stable after 30 days. Surprisingly, the initially sensitive strain remained in all populations and its frequency was highest when phage pressure was strongest. Resistance to phages in these populations emerged initially through mutations preventing capsule biosynthesis. Protection through lysogeny was rarely observed because the lysogens have increased death rates due to prophage induction. Unexpectedly, the adaptation process changed at longer time scales the frequency of capsulated cells in BJ1 populations increased again, because the production of capsule was fine-tuned, reducing the ability of phage to absorb. Contrary to the lysogens, these capsulated resistant clones are pan-resistant to a large panel of phages. Intriguingly, some clones exhibited transient non-genetic resistance to phages, suggesting an important role of phenotypic resistance in coevolving populations. Our results show that interactions between lysogens and sensitive strains are shaped by antagonistic co-evolution between phages and bacteria. These processes may involve key physiological traits, such as the capsule, and depend on the time frame of the evolutionary process. At short time scales, simple and costly inactivating mutations are adaptive, but in the long-term, changes drawing more favorable trade-offs between resistance to phages and cell fitness become prevalent.