We obtain the exact classical algebra obeyed by the conserved non-loca
l charges in bosonic non-linear sigma models. Part of the computation
is specialized for a symmetry group O(N). As it turns out the algebra
corresponds to a cubic deformation of the Kac-Moody algebra. We genera
lize the results for the presence of a Wess-Zumino term. The algebra i
s very similar to the previous one, now containing a calculable correc
tion of order one unit lower. The relation with Yangians and the role
of the results in the context of Lie-Poisson algebras are also discuss
ed.