  It is shown that the Affine Toda models (AT) constitute a ``gauge fixed''
version of the Conformal Affine Toda model (CAT). This result enables one to
map every solution of the AT models into an infinite number of solutions of the
corresponding CAT models, each one associated to a point of the orbit of the
conformal group. The Hirota's $\tau$-function are introduced and soliton
solutions for the AT and CAT models associated to $\hat {SL}(r+1)$ and $\hat
{SP}(r)$ are constructed.
