In order to examine different strategies in the search for more resistant bacterial cultures, we have simulated a variety of growth, mutation, competition and selection processes that may arise in interacting populations of bacteria and phages. Our model considers a culture containing several variants of the same bacterium, each sensitive to attacks from a specific phage. The culture is growing in a chemostat with a continuous supply of nutrients. Surplus bacteria and vira are removed through dilution. Depending on the rate of dilution, the model exhibits a stable equilibrium, self-sustained oscillations, quasi-periodic behavior, deterministic chaos, or extinction of certain species. The model can also be used to describe evolutionary changes in the composition of the microbiological system.