  We have performed some explicit calculations of the conservation laws for
classical (affine) Toda field theories, and some generalizations of these
models. We show that there is a huge class of generalized models which have an
infinite set of conservation laws, with their integrated charges being in
involution. Amongst these models we find that only the $A_m$ and $A_m^{(1)}$
($m\ge 2$) Toda field theories admit such conservation laws for spin-3. We
report on our explicit calculations of spin-4 and spin-5 conservation laws in
the (affine) Toda models. Our perhaps most interesting finding is that there
exist conservation laws in the $A_m$ models ($m\ge4)$ which have a different
origin than the exponents of the corresponding affine theory or the
energy-momentum tensor of a conformal theory.
