The evolution of exploitative specificity can be influenced by environmental variability in space and time and the intensity of trade-offs. Coevolution, the process of reciprocal adaptation in two or more species, can produce variability in host exploitation and as such potentially drive patterns in host and parasite specificity. We employed the bacterium Pseudomonas fluorescens SBW25 and its DNA phage Phi2 to investigate the role of coevolution in the evolution of phage infectivity range and its relation with phage growth rate. At the phage population level, coevolution led to the evolution of broader infectivity range, but without an associated decrease in phage growth rate relative to the ancestor, whereas phage evolution in the absence of bacterial evolution led to an increased growth rate but no increase in infectivity range. In contrast, both selection regimes led to phage adaptation (in terms of growth rates) to their respective bacterial hosts. At the level of individual phage genotypes, coevolution resulted in within-population diversification in generalist and specialist infectivity range types. This pattern was consistent with a multilocus gene-for-gene interaction, further confirmed by an observed cost of broad infectivity range for individual phage. Moreover, coevolution led to the emergence of bacterial genotype by phage genotype interactions in the reduction of bacterial growth rate by phage. Our study demonstrates that the strong reciprocal selective pressures underlying the process of coevolution lead to the emergence and coexistence of different strategies within populations and to specialization between selective environments.