Analogy is heavily used in instructional texts. We introduce the concept of analogical dialogue acts (ADAs), which represent the roles utterances play in instructional analogies. We describe a catalog of such acts, based on ideas from structure-mapping theory. We focus on the operations that these acts lead to while understanding instructional texts, using the Structure-Mapping Engine (SME) and dynamic case construction in a computational model. We test this model on a small corpus of instructional analogies expressed in simplified English, which were understood via a semi-automatic natural language system using analogical dialogue acts. The model enabled a system to answer questions after understanding the analogies that it was not able to answer without them.