Note on the stability in affine Toda field theories

We show that certain vanishing couplings in the Â Ê affine Toda field theories remain vanishing even after higher order corrections are included. This is a requisite property for the lagrangian formulation of the theory. We develop a new perturbative formulation and treat affine Toda field theories as a massless theory with exponential interaction terms. We show that the Dynkin automorphism of the Lie algebra leads to the non-renormalization of the vanishing couplings.