In solitary carnivorous mammals, territoriality is assumed to benefit male fitness by ensuring the exclusivity of matings within territories via mate guarding and female defence. However, this hypothesis remains empirically untested. Here, we examined this hypothesis for solitary territorial carnivores using the Iberian lynx (Lynx pardinus) as a case study. We expected that territorial males sire all litters born within their territories, translating into the absence of multi-paternity cases within the same litter. We analysed parentage in 43 kittens, belonging to 20 different litters. For 42 kittens, a father could be assigned using microsatellites and always coincided with the individual holding the territory. For 16 kittens from 10 litters for which we also had information on SNPs, paternity assignments coincided with microsatellites, except for a litter (two kittens) from the same litter for which a different male was assigned, but the territorial male could not be excluded. Our results indicated that multi-paternity in the Iberian lynx must be a rare event, and that territorial males sire all litters born from the females with which they share territories. We propose that both the low number of mature individuals in the lynx population and the fact that female oestrus is induced by male presence may explain results.