When people hold several objects (such as digits or words) in working memory and select one for processing, switching to a new object takes longer than selecting the same object as that on the preceding processing step. Similarly, selecting a new task incurs task- switching costs. This work investigates the selection of objects and of tasks in working memory using a combination of object-switching and task-switching paradigms. Participants used spatial cues to select one digit held in working memory and colour cues to select one task (addition or subtraction) to apply to it. Across four experiments the mapping between objects and their cues and the mapping between tasks and their cues were varied orthogonally. When mappings varied from trial to trial for both objects and tasks, switch costs for objects and tasks were additive, as predicted by sequential selection or resource sharing. When at least one mapping was constant across trials, allowing learning of long-term associations, switch costs were underadditive, as predicted by partially parallel selection. The number of objects in working memory affected object-switch costs but not task-switch costs, counter to the notion of a general resource of executive attention.