According to a central claim of Kornblum's dimensional-overlap model, response-related processes do not start before stimulus-related processes have been completed, which implies an additive relationship between effects of stimulus-stimulus congruence and stimulus-response compatibility. Three experiments were conducted to test this prediction. In Exp. 1, additive effects of color-word congruence (Stroop effect) and irrelevant spatial S-R compatibility (Simon effect) were in fact obtained. However, interactions between congruence and compatibility were observed in Exp. 2, where flanker-target congruence was varied, and in Exp. 3, where inter-level congruence of multi-level letters was manipulated. It is argued that these findings are inconsistent with the seriality assumption of the dimensional-overlap model, but that they support models claiming a temporal overlap of stimulus and response processing instead.