All perfect praise be to Allaah, the Lord of the worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His Slave and Messenger.
If the questioner means by "unauthentic Hadeeths" the Hadeeths that are falsely attributed to the Prophet, sallallaahu ‘alayhi wa sallam, it is forbidden to narrate these Hadeeths except for the purpose of explaining that they are fabricated. The Prophet, sallallaahu ‘alayhi wa sallam, said: "Whoever deliberately tells a lie on my behalf, let him be assured of his seat in Hell." [Al-Bukhari and Muslim] He, sallallaahu ‘alayhi wa sallam, also said: "Whoever relates from me something which he deems false is one of the liars." [Muslim]
If the questioner means the Dha‘eef (weak) Hadeeth, a group of scholars of Hadeeth and others tolerated narrating weak Hadeeths and acting upon them in matters where belief and rulings are not concerned. This concession was reported from Abdur-Rahmaan ibn Mahdi, Ibn Al-Mubaarak, Ahmad ibn Hanbal, and other scholars of Hadeeth .
Some scholars held the opinion that it is permissible to act according to weak Hadeeth with certain conditions, not absolutely, and this is the preponderant opinion – Allaah willing.
A third group of scholars said that it is not permissible to act according to weak Hadeeths at all.
Allaah Knows best.