Single-task and dual-task versions of verbal and spatial serial order memory tasks were administered to 120 students tested for working memory capacity with four previously validated measures. In the dual-task versions, similarity between the memory material and the material of the secondary processing task was varied. With verbal material, three additional words had to be read aloud in the retention interval, and their phonological and semantic similarity to memory list words was varied orthogonally. With spatial material, choice RT tasks in the retention interval used stimuli from either the same or a different kind as the memory stimuli. Similarity had little effect on dual-task costs. For correlational analyses, individual dual-task costs were measured in various ways, which varied as to their direction of correlation with working memory capacity. In general, these correlations were low. Dual-task costs, although measured reliably, did not correlate across verbal vs. spatial tasks. The results lend little support to theories identifying working memory capacity with the ability to resist interference, or the ability to coordinate two concurrent tasks.