This paper extends binary support vector machines to multiclass classification for recognising emotions from speech. We apply two standard schemes (one-versus-one and one-versus rest) and two schemes that form a hierarchy of classifiers each making a distinct binary decision about class membership, on three publicly-available databases. Using the OpenEAR toolkit to extract more than 6000 features per speech sample, we have been able to outperform the state-of-the-art classification methods on all three databases.