Maamoun Abdulkarim, the head of the Antiquities and Museums Department in Damascus, tells The Associated Press that one of the tombs belongs to Mohammad Bin Ali, a descendant of Islam's Prophet Muhammad's cousin Imam Ali.
Abdulkarim said today that the tomb was just north of Palmyra.
He said the second tomb was of a Sufi scholar known as Nizar Abu Bahaa Eddine, who was in the town 500 years ago. The tomb is close to the town's famed archaeological site.
Since the Islamic State group captured Palmyra last month, there have been fears that the extremists would blow up archaeological sites as they have in Iraq.