Two experiments with a working-memory updating task investigated dual-task interference between short-term storage of numerical and spatial material, between execution of a numerical and a spatial updating operation, and between storage and processing. Participants memorised a set of digits and a set of spatial positions, updated elements of both sets by a sequence of operations, and then recalled the final values. In Experiment 1, a single element in each memory set had to be updated several times. There was little interference between storage of the two sets, and between storage and processing, but parallel execution of the two operations was not possible. In Experiment 2, all elements in both memory sets were updated in random order. There was substantial interference between memory for the numerical and the spatial sets, and between storage and processing. Parallel execution of two operations was again not possible. Moreover, trying to do two operations simultaneously resulted in impaired memory of final results. The results support the distinction between the activated part of long-term memory that can hold elements currently not needed for processing, and a more central, capacity-limited part of working memory that provides access to its contents for processing.