What are the conditions for accepting a Hadith according to Al-Bukhari and Muslim?

Al-Bukhari and Muslim did not explicitly state a condition in their books, but their condition was known through empirical examination, and the imams differed on this matter.

Abu Al-Fadl ibn Tahir said: "Their condition is to include hadith where there is agreement on the reliability of its narrators up to the well-known Companion, and that its chain of narration is connected and not interrupted."

Abu Bakr Al-Hazimi said: "The condition for a sound (sahih) hadith is the continuity of the chain of narration, and that the narrator be a Muslim, truthful, not a fabricator (mudallis), nor confused, characterized by justice, precision, and soundness of belief."

He added that Al-Bukhari's condition is to include what has a connected chain of narration from precise and highly reliable narrators who had a long association with those from whom they took knowledge. He may sometimes include from the next stratum in terms of precision.

As for Muslim, he includes the hadiths of both strata comprehensively. He may also include a hadith from someone who was not free from the defects of disparagement (jarh) if he had a long association with the one from whom he took knowledge.

Ibn Al-Jawzi said: "Al-Bukhari and Muslim stipulated reliability and renown. They omitted hadiths that should not have been omitted, such as Al-Bukhari's omission of narrations from Hammad ibn Salama and Suhayl ibn Abi Salih."