The effects of Simon-and Stroop-like stimuli are examined in isolation and in factorial combinations with different delays between the presentation of the irrelevant and the relevant stimuli. The effects of irrelevant stimuli have different time courses depending on whether they overlap with the relevant stimulus (stimulus-stimulus overlap, Dimensional Overlap [DO] Type 4) or with the response (stimulus-response overlap, DO Type 3). A new, computational, parallel distributed processing (PDP)-type model, DO'97, is presented that is based on the original DO model (S. Kornblum, 1994;S. Kornblum, T. Hasbroucq, & A. Osman, 1990), and it postulates a nonmonotone irrelevant stimulus activation function in addition to 2 temporally ordered, serial, nonindependent stages: a stimulus processing stage and a response production stage. DO'97 is able to simulate the temporal dynamic characteristics of the processes, with good fits to the empirical data of this study and other published studies, at the level of means, variances, and distributional plots.After decades of empirical, and generally fragmented, research on stimulus-stimulus (S-S) and stimulus-response (S-R) compatibility effects, attempts have recently been made to understand the broad theoretical underpinnings of this large class of phenomena. Some of these attempts, instead of treating each effect in isolation, as had been done in the past, have tried to identify the processing principles that they have in common. Thus, by carefully examining these effects, particularly the effects of irrelevant stimuli, many similarities have become apparent. For example, when the irrelevant aspects of a stimulus are consistent with the relevant aspects either of the stimulus or of the response, reaction times (RTs) tend to be faster than when they are inconsistent (for reviews see Prinz, 1997, andProctor &Reeve, 1990). 1 Different combinations of such consistency relationships produce the so-called Stroop effect (for a review see MacLeod, 1991), the Simon effect (for a review see Simon, 1990), and other compatibility effects.