Intelligent problem solving systems must be able to express their results in a coherent and flexible manner. One way this can be done is by eztemporaneous elaboration, the method of language production that underlies more skilled tasks such as explanation. This paper outlines a computational model for extemporaneous elaboration that is implemented in a computer model called Extemper, shows examples of its operation, and compares it with other models of language production. Extemper contains the four components minimally required for elaboration: 1) an efficient method for linearizing a knowledge structure, 2) a translation/selection mechanism for producing a conceptual textbase from the knowledge structure, 3) local coherence operators which provide local connections between textbase elements, and 4) a conceptual generator to translate the coherent textbase into English.