Based on the weakness of ZG off-line TTP（trusted third party） non-repudiation protocol because of using pro-tocol deadline

the improvement of the ZG off-line TTP non-repudiation protocol was given

which eliminated the delay-ing resolve request attack and ensured non-repudiation and fairness.Therefore

two kinds of improvement of ZG off-line TTP non-repudiation protocol were given

which had different point of focus.Among them

the first one could eliminate delaying message attack in ZG protocol;the second one also had the property of preventing the abuse of sub-protocol be-sides eliminating delaying message attack.The first one is suitable for electronic payment and certified email

but the second one is suitable for digital contract signature.