Encountering a cognitive conflict not only slows current performance, but it can also affect subsequent performance, in particular when the conflict is induced with bivalent stimuli (i.e., stimuli with relevant features for two different tasks) or with incongruent trials (i.e., stimuli with relevant features for two response alternatives). The post-conflict slowing following bivalent stimuli, called "bivalency effect", affects all subsequent stimuli, irrespective of whether the subsequent stimuli share relevant features with the conflict stimuli. To date, it is unknown whether the conflict induced by incongruent stimuli results in a similar post-conflict slowing. To investigate this, we performed six experiments in which participants switched between two tasks. In one task, incongruent stimuli appeared occasionally; in the other task, stimuli shared no feature with the incongruent trials. The results showed an initial performance slowing that affected all tasks after incongruent trials. On further trials, however, the slowing only affected the task sharing features with the conflict stimuli. Therefore, the post-conflict slowing following incongruent stimuli is first general and then becomes conflict-specific across trials. These findings are discussed within current task switching and cognitive control accounts.