In response to predation pressure by raptors, snakes, and carnivores, primates employ anti-predator behaviours such as avoiding areas of high predation risk, cryptic behaviour and camouflage, vigilance and group formation (including mixed-species associations), and eavesdropping on other species’ alarm calls. After detecting a predator, primates can produce alarm calls, show predator-specific escape strategies or even mob the predator. It remains unclear how solitary nocturnal primates respond to diurnal predation pressure while they sleep or rest. The aim of this study was to investigate the diurnal anti-predator behaviour of the nocturnal and solitary Sahamalaza sportive lemur, Lepilemur sahamalazensis, which regularly rests in exposed locations. We observed the responses of 32 Sahamalaza sportive lemurs to playbacks of territorial calls of an aerial predator (Madagascar harrier hawk), mating calls of a terrestrial predator (fossa), and the contact calls of a medium-sized bird (crested coua) as a control, at different diurnal sleeping sites. Lemurs never showed a flight response after replays of predator or control calls, but regularly froze after harrier hawk calls. Lemurs scanned the sky immediately after playback of harrier hawk calls, and the ground or trees after fossa calls. Lemur vigilance increased significantly after both predator calls. After crested coua calls the animals became significantly less vigilant, suggesting that contact calls of this bird serve as indicators of predator absence. We found no response differences between different types of sleeping sites. Our results show that resting Sahamalaza sportive lemurs recognise predator vocalisations as indicators of increased predation risk, discern vocalizations of different predators, and employ anti-predator behaviours specific for different predator classes. Their behavioural responses while resting or sleeping are comparable to those of active primates, and their response rate of 80% shows that this solitary and nocturnal primate is constantly aware of its environment.