<p>Prey animals adjust their vigilance to the level of threat they perceive in their environment. Here, a simple theoretical model studies how the vigilance of an animal may, in turn, influence the behaviour of its predators. By emphasizing the role played by surprise in the hunting success of many predators, the model shows how strongly the chance of being detected can modify the successive phases of a hunting episode. In that respect, a predator attacking a highly vigilant prey will launch its attack from a long distance, even if undetected, and will withdraw if detected before this distance is reached. By contrast, when the prey is less vigilant, the predator will try to approach nearer before launching its attack, and detection by the prey during the approach phase may trigger an immediate attack. A prey animal can thus modify, through its vigilance, the level of risk it actually endures, by influencing the behaviour of its predators. By increasing its level of vigilance, it will not only increase its chance of escape when under an attack, but also make the predators more reluctant to extend their approaches, which decreases their chances of success. Attacks will thus be both less frequent and less deadly. In addition, the prey, which deters the predators from attacking, also spends less time in vain pursuits. The model thus highlights a possible gain in energy associated with vigilance behaviour.</p>