How might two species in a predator-prey relationship coevolve?

Predator-prey relationships, or organism-disease from another point of view, may lead to coevolution as a response to the counterpart affect they have on each other. For example, as a predator pressures a community of preys by running after them during the day, the preys may tend to stay out only at night and those that are better prepared for the night will prevail. This phenomenon leads to a community of preys that comes out at night more than the day. On the other hand, the opposite may happen as the predator will need to come out at night more than it did before. As both species evolve to adapt to each other's pressure over them, evolution occurs on both sides. This is coevolution.