The present dual-task study used lateralized readiness potentials (LRPs) and behavioral measures to determine whether response activation for Task 1 and Task 2 can occur in parallel. We also examined whether task similarity (known as dimensional overlap) increases parallel central processing by making it difficult to selectively activate one task set. With dimensional overlap, the behavioral data replicated previous findings of backward correspondence effects: The Task 1 response was influenced by its compatibility with the Task 2 response. This finding suggests parallel response activation. The LRP data supported this conclusion: Task 2 response activation (indexed by the LRP) began before Task 1 central operations had finished. When there was no dimensional overlap, backward correspondence effects could not be measured, but the LRP data confirmed that parallel response activation still occurred. We argue that parallel response activation does occur, perhaps due to accidental activation of Task 2 mapping rules when the intention is to selectively execute Task 1 mapping rules.