The gold standard for diagnosing sleep apnoea-hypopnoea syndrome (SAHS) is polysomnography (PSG), an expensive, labour-intensive and time-consuming procedure. Accordingly, it would be very useful to have a screening method to allow early assessment of the severity of a subject, prior to his/her referral for PSG. Several differences have been reported between simple snorers and SAHS patients in the acoustic characteristics of snoring and its variability. In this paper, snores are fully characterised in the time domain, by their sound intensity and pitch, and in the frequency domain, by their formant frequencies and several shape and energy ratio measurements. We show that accurate multiclass classification of snoring subjects, with three levels of SAHS, can be achieved on the basis of acoustic analysis of snoring alone, without any requiring information on the duration or the number of apnoeas. Several classification methods are examined. The best of the approaches assessed is a Bayes model using a kernel density estimation method, although good results can also be obtained by a suitable combination of two binary logistic regression models. Multiclass snore-based classification allows early stratification of subjects according to their severity. This could be the basis of a single channel, snore-based screening procedure for SAHS.