As two special digital signatures, group signature and designatedverifier signature play very important roles in the e-commerce. A group signature scheme allows a group member to anonymously sign message on behalf of the group, In case of a dispute, the group manager can reveal the actual identity of signer. Group signature is widely used in e-cash, e-voting, e-bid and so on. In a designated verifier signature scheme, only the designated verifier can verify the validity of a signature. Thus, the designated verifier signature is widely applied in the copyright-protect. Recently, Zhou et.al presented a dynamicgroup signature scheme with forward security, and Zhang et.al gave an efficient ID-based designated verifiersignature scheme. Unfortunately, in this work we show that Zhou et.al's group signature is universally forgeable, Namely, any one can forge a group signature on another message by a given signature, then an improved vision is presented; And we also show that Zhang et.al's scheme is delegatable, namely, a third party can produce a signature on message m by the revealed side information. Finally, we give the corresponding attack on the two signature schemes.