[en] In Li Yishen and Zhu Guocheng (1985) we defined directly the new set of symmetries for KdV equations and proved that they constructed a Lie algebra with the ''old'' symmetries. We also pointed out the relation between new symmetries and non-isospectral evolution equations. In this paper, we show the same results for AKNS system and discuss the NLS equations, MKdV equations, S-G equations and Sinh-G equations in the reduced problem. For the latter three equations we obtain more symmetries than in Chen, Lee and Lin. (author)