In polygynous ungulates, the rut imposes constraints on male time budgets that generate a trade-off between maintenance and reproduction, leading to a reduction in time spent foraging. As mating activities can incur substantial somatic costs, males are expected to spend their ‘non-rutting’ time recovering during the breeding season. If the diminution in time allocated to foraging by males is only a consequence of time budget constraints, males should keep a similar ratio of time spent foraging to lying to that observed in the pre-rut, leading to an overall reduction of these two activities (the ‘foraging constraint’ hypothesis). Alternatively, if males adopt an energy-saving strategy, they should limit energy expenditures by reducing foraging but not lying time, as the energy gains of forage intake may not meet the basal energetic requirements, especially in northern and temperate regions (the ‘energy-saving’ hypothesis). Here, we contrast these two hypotheses by comparing individual daily time budgets of marked adult bighorn sheep rams (Ovis canadensis) and male mountain goats (Oreamnos americanus) during the pre-rut and the rut. Concordant results for both species support the ‘foraging constraint’ hypothesis, as sexually-active males reduced time spent foraging and lying from the pre-rut to the rut because of an increase in time spent in mating-related activities. Bighorn sheep rams also increased time spent foraging when not engaged in mating tactics, providing further support for a ‘maximisation’ of energy intake in the absence of reproductive opportunities. Because there are also known physiological changes that occur during the rut which may cause appetite suppression, for example to produce metabolic compounds linked with olfactory communication (the ‘scent-urination’ hypothesis) or to cope with increased burden of parasites (the ‘parasite-induced anorexia’ hypothesis), further research should aim at simultaneously testing these current hypotheses to better understand rut-induced hypophagia and its effects on the life histories of male ungulates.