Cognitive control adjusts information processing to momentary needs and task requirements. We investigated conflict adaptation when participants are performing two tasks, a Simon task and a SNARC task. The results indicated that one congruency effect (e.g., Simon) was reduced after conflict in the other task (e.g., SNARC), but only when both tasks used identical relevant information. On the other hand, when both tasks used different relevant information, a larger congruency effect was observed after conflict in the other task. The results are explained in terms of a local control mechanism.