Abstract
The authors define directly a new set of symmetries for the AKNS system and prove that they constitute an infinite-dimensional Lie algebra with the 'old' symmetries. They also point out the relation between the new symmetry and the non-isospectral problem. They use the reduction technique and point out that the NLS, MKdV, SG and sinh-G hierarchies have two sets of symmetries which constitute an infinite-dimensional Lie algebra. These results are extensions of those of Chen et al. (1982).