AbstractThe competitive exclusion principle is fundamental to understanding coexistence. Well‐established theories predict the conditions for coexistence in consumer–resource interactions. Given that species often compete for commodities offered by mutualists, competitive exclusion theory should also be critical to understanding how mutualisms function. We explicitly apply the competitive exclusion principle to mutualism and derive a rule analogous to Tilman's R* rule for exploitative competition. Coexistence is impossible when competitors compete solely for a shared partner‐provided commodity because superior competitors deplete that commodity sufficiently to exclude inferior competitors. We then investigate how competition between two guild members for a partner‐provided commodity and a resource external to the mutualism affects competitor coexistence. There are three key results. First, coexistence is possible via partitioning of a partner‐provided commodity and another resource. Second, unlike in classic R* Theory, competitive outcomes are influenced both by species’ abilities to obtain commodities and their mutualisms with the shared commodity‐providing partner, which can indirectly alleviate competitors’ commodity limitation. Third, the outcome of competition has important consequences for the commodity‐providing partner, which depend on the type of mutualism and the competitive abilities of competing mutualists. This theory provides a novel framework for investigating how competitors for mutualistic commodities coexist in nature.