The measurement of "switch costs" is held to be of interest because, as is widely believed, they may reflect the control processes that are engaged when subjects switch between two (or more) competing tasks. [In task-switching experiments, the reaction time (RT) switch cost is typically measured as the difference in RT between switch and non-switch (repeat) trials.] In this report we focus on the RT switch costs that remain even after the subject has had some time to prepare for the shift of task, when the switch cost may be approximately asymptotic (so-called residual switch costs). Three experiments are presented. All three experiments used Stroop colour/word, and neutral stimuli. Participants performed the two tasks of word-reading and colour-naming in a regular, double alternation, using the "alternating runs" paradigm (R. D. Rogers & S. Monsell, 1995). The experiments were designed to test the hypothesis that RT switch costs depend on a form of proactive interference (PI) arising from the performance of a prior, competing task. A. Allport, E. A. Styles and S. Hsieh (1994) suggested that these PI effects resulted from "task-set inertia", that is, the persisting activation-suppression of competing task-sets, or competing task-processing pathways. The results confirmed the existence of long-lasting PI from the competing task as a major contributor to switch costs. Non-switch trials, used as the baseline in the measurement of switch costs, were also shown to be strongly affected by similar PI effects. However, task-set inertia was not sufficient to account for these results. The results appeared inconsistent also with all other previous models of task switching. A new hypothesis to explain these between-task interference effects was developed, based on the stimulus-triggered retrieval of competing stimulus-response (S-R) associations, acquired (or strengthened) in earlier trials. Consistent with this retrieval hypothesis, switch costs were shown to depend primarily on the S-R characteristics of the preceding task (the task that was switched from) rather than the upcoming task. Further, the effects of the other, competing task were found to persist over many successive switching trials, affecting switch costs long after the stimulus overlap (and hence the principal S-R competition) between the current tasks had been removed. Switch costs were also found to be affected by recent, item-specific experience with a given stimulus, in either the same or the competing task. Finally, the results showed that switch costs were massively affected by the ratio of the number of prior trials, in response to the same stimuli, that had implemented either the currently intended or the competing S-R mappings. None of these effects are predicted by current models of residual switch costs, which appeal to the differences in control processes assumed to be engaged in switch versus non-switch trials.