This paper explores the possibilities of using Hidden Markov Models to represent, and to recognise, the tones in connected Modern Standard Chinese speech. The paper is based on data consisting of some 400 (currently being extended to 1000) syllables of connected speech by a single speaker. It has recently been shown (Yang et al. 1988) that HMM techniques can be used successfully to model the tones in isolated syllables, but the problem with the tones in connected speech is that they are subject to a good deal of variation. Syllable stress is one important conditioning factor involved in this variation.