This paper provides a solution to discourse structure adaptation in the process of automatic hypermedia presentation generation. Existing approaches to discourse structure composition are based on the assumption that a user can comprehend relations between the elements in a discourse structure if the overall structure is semantically coherent. This assumption does not, so far, take into account specific user needs. In this paper we show that although discourse structure composition approaches significantly differ, a general model of the composition process can be derived. Within this general model we identify how adaptation can be applied. We formulate the problem of discourse adaptation with regard to the general model and present our proposed solution.