The study considers the discourse functions of intonation and identifies a few problems and contradictions in the current theories of intonation functioning. Particular attention is paid to such issues as the multiple functions of nuclear tones, pitch declination in utterances and perceptual identification of spoken paragraphs. An attempt has been made to handle these problems in the context of English public speeches delivered in the format of TED talks. The purpose of the auditory analysis of discourse intonation in these talks is to check the perceptual reliability of intonation cues in processing spoken discourse and the possibility of using intonation as an on-line perception strategy. The methods applied in the research are descriptive, auditory and comparative, supported by a certain amount of quantitative data. The results obtained in the auditory analysis show that intonation cues work most effectively at the level of intonation groups and utterances but are not self-sufficient in paragraph identification. The leading function of nuclear tones in public discourse organization turns out to be the information structuring of utterances, which is occasionally interrupted by the attitudinal function. Pitch declination has been found to be one of the most important cues to the integrity and cohesion of utterances, with an average length of three-four intonation groups. Multiple declinations in spoken utterances are infrequent and are triggered by particular types of syntactic relations in elongated sentences. The study contributes to the linguistic description of discourse intonation, and its results can be beneficial for language teaching practice and automated speech synthesis.