Large language models (LLMs) significantly influence many spheres of life: education, creativi-ty, science, and business. This paper considers the use of LLMs to explain alternative solutions obtained by a decision support system under uncertainty. Classical and pragmatic models of explanation proposed by phi-losophers are discussed. The goals and tasks of explanation in decision support processes under uncertainty are formulated. The operation of LLMs is conceptually analyzed, and their current capabilities in solving typical test tasks are assessed. The main techniques of prompting (a system of queries to a language model) are considered; with these techniques, a language model can be tuned to generate explanations for alternative solutions to particular tasks in a subject area. Finally, prompt techniques for supporting pragmatic and clas-sical theories of explaining alternative solutions are considered.