In dual-task experiments, overlapping response characteristics of two subsequently performed tasks may not only affect performance in Task 2 but also in Task 1. This phenomenon is often explained through activated Task 2 response information influencing Task 1 response selection, which then possibly propagates again into Task 2. So far, however, only little is known about (a) the time course of this Task 2 response activation and (b) possible transmission/propagation mechanisms. The present study addressed both issues by testing 10 plausible drift-diffusion models with 5 data sets from dual-task experiments. To this end, we first examined if the temporal course of the response activation is linearly increasing or pulse like. The pulse-like model turned out to be superior, but the corresponding dynamics of the response activation often described a monotonically increasing function that reached its peak late during Task 1 processing. By extending the pulse-like model with an additional diffusion process, we then examined whether and how the Task 2 response information could affect subsequent Task 2 response selection. Concerning the transmission mechanisms, none of the assumed models proved to be entirely satisfactory. However, additional simulations suggest that Task 2 response activation-transmission does not occur at all. Instead, a model in which Task 2 started with a trace of the previous Task 1 response (i.e., irrespective of the preexisting Task 2 activation) turned out to be the most promising account. (PsycInfo Database Record (c) 2023 APA, all rights reserved).