I am using Neo-gui. I imported my key from Ico when it was Antshare.
I don't understand if neo-gui is a deterministic wallet for the new addresses or have I to save every private key?
NEO-GUI is non-deterministic wallet, so you'll have to save every new private key generated.
What do you mean by every private key? You got a private key from your old wallet, right? You can just use this one for the new one. Maybe you should try NEON wallet or Neotracker.io what is much easier than the NEO GUI to be honest.
Deterministic wallets are wallets that derive all private keys from single huge random number called seed. This derivation process is deterministic meaning that the same seed value will always generate the same set of private keys. As seed is sufficient to recover all private keys, it is the only thing that has to be backed up. Seeds are typically encoded as string of English words. Most Bitcoins wallets are deterministic wallets. Non-deterministic wallets are wallets that contains set of randomly and independently generated private keys. As private keys generated by this type of wallet are unrelated, each and every one of them has to be backed up separately. NEO-GUI is non-deterministic wallet.