The Dimension Action (DA) model asserts that the visual system is modular, and that each task involves multiple-response mechanisms rather than a unitary-response selection mechanism. The model has been supported by evidence from single-task interference paradigms. We use the psychological refractory period paradigm and show that dual-task performance can also be explained by the DA model. In 6 experiments we contrasted predictions from the DA model with predictions from the Response Selection Bottleneck (RSB; Pashler, 1994) model asserting that dual-task limitations are due to a unitary-response selection mechanism. Task 1 in all experiments was a tone discrimination task. In Experiments 1 to 3, Task 2 was a variation of either the Stroop or the flanker tasks. Experiments 4 to 6 manipulated response selection directly. The results showed that response selection effects can be underadditive in some conditions and additive in others depending on the modular nature of the response effect. Together, the results support the existence of an underlying modular architecture as proposed by the DA model and pose serious difficulties for the RSB model. (Contains 8 tables and 5 figures.)