The narrations regarding Imam Hasan  and Imam Hussein (AS) offering prayers behind Marwan have been narrated in Shia sources with two different chains. One of the narrations has been narrated from Imam Ja'far Sadiq (AS) and the other from Imam Musa bin Ja'far (AS).
The first narration has been mentioned in Rawandi's book titled "al-Nawadir". However, the translation of the narration is as such: Imam Sadiq (AS) said: "Hasan and Hussein (AS) prayed many times behind Marwan al-Hakam. One of them was asked as to whether or not his father repeated his prayers when he arrived back home (because he had offered prayers behind those unjust people) to which he replied, "No, by Allah, because they did not add a verse (from the Quran) to the prayer."[1]
As for the second narration, Ali bin Ja'far quotes a lengthy narration  from Musa bin Ja'far.[2] Sheikh Hurr Amili (ra) narrates that part of the narration which is under discussion as such: "Imam Musa bin Ja'far (AS) said, "Imam Hasan and Imam Hussein, peace be upon them, prayed behind Marwan and we also pray behind them (i.e. the oppressive and unjust rulers).[3]
Late Rawandi cites the first narration from a book titled al-Ja'fariyat (al-Ash'athiyat): Muhammad bin Muhammad bin Ash'ath al-Kufi has narrated that when he went to Egypt, he attended a lesson (class) taught by Musa bin Ismail son of Musa bin Ja'far and it was there and then that he decided to write a book in a bid to narrate most of the narrations which he had heard from Musa bin Ismail son of Musa bin Ja'far. It is noteworthy that the said narration has been narrated by him in his book with the same isnad (chain of transmission) by him from Imam Sadiq (AS).  According to Allamah Hilli, Najashi and other Shiite scholars, he is a reliable person amongst Shiite scholars.
As well, based on the researches conducted into the chain of the transmitters of the second narration, it should be said that the said narration is authentic and all the narrators of the tradition are Twelver Shiites, just ('adil) and accurate (dhabit).
The important question that has to be dealt with here is: Why were the Infallible Imams (AS) praying behind such people? The answer is that the Imams offered prayers behind them under taqiya. Sheikh Hurr Amili has mentioned the said narration in the chapter about the "desirability of attending, under taqiyah, a congregational prayer behind a person who should not be followed in prayers". [4]
It is pertinent to mention that one of highly important concepts in the Shiite school of jurisprudence is taqiya which literally means to guard and protect oneself against any harm but technically it means to hide the truth and conceal one's belief in the truth and not to expose one's faith to the opponents as well as not to do anything in front of them that would result in any harm to your religion or your worldly interests. In fact, taqiya is a calculated tactic for protection of human forces and preventing any harm for petty and insignificant issues. There are a lot of narrations about taqiya of which we shall suffice to mentioning only a few.
1. Imam Baqir (AS) says: "Taqiya or precautionary dissimulation is my religion and the religion of my fathers. He who does not practice taqiya has no faith."[5]
2. Imam Sadiq   (AS) says: "God could not be better worshipped than by taqiya."[6]
3. Sheikh Saduq narrates from Imam Sadiq (AS) that he said, "If you say that he who abandons taqiya is like one who abandons prayer, you have told the truth."[7]

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