This paper examines the problem of automatic explanation of reasoning, or the ability of a program to discuss what it is doing in some understandable way, particularly as part of an expert system. An introduction presents a general framework in which to view explanation and reviews some of the research in this area. This is followed by a discussion of the motivation for strategic explanations in two diagnostic consultation programs, MYCIN and NEOMYCIN. Design criteria for automatic explanations of reasoning are outlined. It is noted that an automatic explanation of program strategy is usually concrete (referring to aspects of the current problem situation) but that abstract explanations (articulating a general principle that can be applied in different situations) are useful in teaching and explaining by analogy. The aspects of NEOMYCIN that make abstract strategic explanations possible, i.e., the representation of strategic (program controlling) knowledge explicitly and separately from domain (subject) knowledge, are described, as are its strategic "why" and "how" explanations. Implementation issues and future work on NEOMYCIN's explanation system are also discussed, and it is noted that the long-range goal of this research is to use NEOMYCIN as the foundation of a teaching system. The paper includes a 29-item bibliography and a list of names and addresses of government and private sector research/information centers and personnel concerned with computer-aided instruction. (Author/ESR)