Current research on analogy processing assumes that different conceptual relations are treated similarly. However, just as words and concepts are related in distinct ways, different kinds of analogies may employ distinct types of relationships. An important distinction in how words are related is the difference between associative (dog-bone) and categorical (dog-cat) relations. To test the hypothesis that analogical mapping of different types of relations would have different neural instantiations, we tested patients with left and right hemisphere lesions on their ability to understand two types of analogies, ones expressing an associative relationship and others expressing a categorical relationship. Voxel-based lesion-symptom mapping (VLSM) and behavioral analyses revealed that associative analogies relied on a large left-lateralized language network while categorical analogies relied on both left and right hemispheres. The verbal nature of the task could account for the left hemisphere findings. We argue that categorical relations additionally rely on the right hemisphere because they are more difficult, abstract, and fragile, and contain more distant relationships. (Contains 3 figures and 2 tables.)