Some prior research has shown that emotion impairs logicality in deductive reasoning tasks, while other research suggests improved performance with emotional contents. We suggest that relevance, whether the affective state is associated with the semantic contents of the reasoning task, may be crucial in explaining these apparently inconsistent findings. This hypothesis is based on a framework distinguishing between integral emotions, where affective responses are evoked by the semantic contents of the target task, and incidental emotions, where affective responses are not related to the task. In 4 experiments we examined the effect of emotion on conditional reasoning when affective responses were relevant and irrelevant. We used images presented simultaneously with the reasoning stimuli (Experiments 1, 2, and 3) or videos presented prior to the reasoning stimuli (Experiment 4) that were either emotional or neutral and semantically related or not to the conditional statements. Results showed that emotion decreased the proportion of normatively correct responses only in the irrelevant condition. In the relevant condition, emotion did not produce reliable deleterious effects. We used reaction time and skin conductance measures to investigate the physiological and cognitive correlates of these effects. Results are discussed in terms of the distinction between incidental and integral emotions.