Camera trap data are increasingly being used to characterise relationships between the spatiotemporal activity patterns of sympatric mammal species, often with a view to inferring inter-specific interactions. In this context, we attempted to characterise the kleptoparasitic and predatory tendencies of spotted hyaenas Crocuta crocuta and lions Panthera leo from photographic data collected across 54 camera trap stations and two dry seasons in Tanzania's Ruaha National Park. We applied four different methods of quantifying spatiotemporal associations, including one strictly temporal approach (activity pattern overlap), one strictly spatial approach (co-occupancy modelling), and two spatiotemporal approaches (co-detection modelling and temporal spacing at shared camera trap sites). We expected a kleptoparasitic relationship between spotted hyaenas and lions to result in a positive spatiotemporal association, and further hypothesised that the association between lions and their favourite prey in Ruaha, the giraffe Giraffa camelopardalis and the zebra Equus quagga, would be stronger than those observed with non-preferred prey species (the impala Aepyceros melampus and the dikdik Madoqua kirkii). Only approaches incorporating both the temporal and spatial components of camera trap data resulted in significant associative patterns. The latter were particularly sensitive to the temporal resolution chosen to define species detections (i.e. occasion length), and only revealed a significant positive association between lion on spotted hyaena detections, as well as a tendency for both species to follow each other at camera trap sites, during the dry season of 2013, but not that of 2014. In both seasons, observed spatiotemporal associations between lions and each of the four herbivore species considered provided no convincing or consistent indications of any predatory preferences. Our study suggests that, when making inferences on inter-specific interactions from camera trap data, due regards should be given to the potential behavioural and methodological processes underlying observed spatiotemporal patterns.