Evidence from task-switching research suggests that task representations passively decay over time, as demonstrated by studies manipulating the response-cue interval (RCI). This time interval does not allow for active preparation of the upcoming task, but provides time for the current representation to decay. As a result, switch costs (worse performance in task switches compared to task repetitions) tend to decrease with increasing RCIs. The present study aims to investigate the temporal dynamics of higher-order cognitive representations in dual-task contexts, where two tasks are jointly represented as a task-pair set. To this end, we will adopt the task-pair switching logic, involving three speeded categorization tasks combined into two task-pairs. Each trial, preceded by a cue, will consist of a task-pair including a constant task 1 (A: tone task), followed by a varying task 2 (B or C: visual tasks). The task-pair sequence will be manipulated on a trial-by-trial basis, resulting in either task-pair switch trials (e.g., AB → AC) or task-pair repetition trials (e.g., AB → AB). We will manipulate both the stimulus-onset asynchrony (SOA: the interval between the onsets of task 1 and task 2 stimuli) and the RCI. Besides a typical effect of SOA, we predict task-pair switch costs in task 1 and task 2 as well as a reduction of these costs with increasing RCIs, as measured by reaction times and error rates. Such findings would suggest that task-pair set activation decays over time, providing new insights into the cognitive mechanisms underlying the reduction of task-pair set activation.