Despite the domestication of sheep and goats by humans for several millennia, we still lack comparative data on their cognitive capacity. Comparing the cognitive skills of farm animals can help understand the evolution of cognition. In this study, we compared the performances of sheep and goats in inference by exclusion tasks. We implemented two tasks, namely a cup task and a tube task, to identify whether success in solving the task could be attributed to either low-level mechanisms (avoiding the empty location strategy) or to deductive reasoning (if two possibilities A and B, but not A, then it must be B). In contrast to a previous study comparing goats and sheep in a cup task, we showed that both species solved the inferential condition with high success rates. In the tube task, performances could not be explained by alternative strategies such as avoiding the empty tube or preferring the bent tube. When applying a strict set of criteria concerning responses in all conditions and controlling for the potential effects of experience, we demonstrate that two individuals, a goat and a sheep, fulfil these criteria. This suggests that sheep and goats are able to make inferences based on deductive reasoning.