  We present a definition of the non-abelian generalisations of affine Toda
theory related from the outset to vertex operator constructions of the
corresponding Kac-Moody algebra $\gh$. Reuslts concerning conjugacy classes of
the Weyl group of the finite Lie algebra $\fing$ to embeddings of $A_1$ in
$\fing$ are used both to present the theories, and to elucidate their soliton
spectrum. We confirm the conjecture of \cite{OSU93} for the soliton
specialisation of the Leznov-Saveliev solution. The energy-momentum tensor of
such theories is shown to split into a total derivative part and a part
dependent only on the free fields which appear in the general solution, and
vanish for the soliton solutions. Analogues are provided of the results known
for the classical solitons of abelian Toda theories.
