Contemporary approaches to automatic speech summarisation comprise several components, among them a linguistic model (LiM) component, which is unrelated to the language model used during the recognition process. This LiM component assigns a probability to word sequences from the source text according to their likelihood of appearing in the summarised text. In this paper we investigate LiM topic and stylistic adaptation using combinations of LiMs each trained on different adaptation data. Experiments are performed on 9 talks from the TED corpus of Eurospeech conference presentations, as well as 5 news stories from CNN broadcast news data, for all of which human (TRS) and speech recogniser (ASR) transcriptions along with human summaries were used. In all ASR cases, summarisation accuracy (SumACCY) of automatically generated summaries was significantly improved by automatic LiM adaptation, with relative improvements of at least 2.5% in all experiments.