In task switching, a conflict between competing task-sets is resolved by inhibiting the interfering task-set. Recent models have proposed a framework of the task-set as composed of two hierarchical components: abstract task identity (e.g., respond to quantity) and more concrete task rules (e.g., category-response rules mapping the categories “one” and “three” to the left and right keys, respectively). The present study explored whether task-set inhibition is the outcome of a general control process or whether it reflects multiple inhibitory processes, each targeting a different component of the competing task-set. To this end, two effects of task-set inhibition were examined: backward inhibition (BI), reflecting the suppression of a just-performed task-set that is no longer relevant; and, competitor rule suppression (CRS), reflecting the suppression of an irrelevant task-set that generates a response conflict. In two task switching experiments, each involving three tasks, we asked participants to make two responses: a cue response, indicating the identity of the relevant task (e.g., “Color”), and a target response requiring the implementation of the task rule (e.g., “Red”). The results demonstrate that BI, but not CRS, appears in cue responses, and thus, suggests that BI reflects inhibition that influences representations related to abstract task identity, rather than (just) competing responses or response rules. These results support a dissociation between inhibitory processes in task switching. The current findings also provide further evidence for a multi-component conceptualization of task-set and task-set inhibition.