Three dual-task experiments were conducted to examine whether the underadditive interaction of the Simon effect and stimulus onset asynchrony (SOA) on Task 2 performance is due to decay. The experiments tested whether the reverse Simon effect obtained with an incompatible stimulus-response (S-R) mapping would show an overadditive interaction with SOA, as predicted by R. De Jong, C.-C. Liang, and E. Lauber's (1994) dual-process model. Tone or letter identification tasks with vocal or keypress responses were used as Task 1. Task 2 was keypresses to arrow direction (or letter identity in Experiment 1). For all experiments, the normal Simon effect showed an underadditive interaction with SOA, but the reverse Simon effect did not show an overadditive interaction. The results imply that the dual-process model is not applicable to the dual-task context. Multiple correspondence effects across tasks implicate an explanation in terms of automatic S-R translation.