Swedish scientist Ake Sellstrom and Angela Kane, the UN high representative for disarmament, arrived at a hotel in the Syrian capital.
The pair are to hold talks with senior government officials during their two-day visit, Damascus-based UN media and communications analyst Khaled Al Masri told AFP.
Top of the agenda will be access to areas of the country where chemical weapons are alleged to have been used so that they can pursue their investigations.
A source close to the UN delegation told AFP on condition of anonymity that the experts were likely to meet Foreign Minister Walid Muallem later today.
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On June 11, the United Nations accepted an invitation from the Syrian government for a visit by the two officials for talks on chemical weapons.
UN spokesman Martin Nesirsky gave a limited brief for the visit at the time.
The two officials accepted the invitation "with a view to completing the consultations on the modalities of cooperation required for the proper, safe and efficient conduct of the UN mission to investigate allegations of the use of chemical weapons in Syria," he said.
Longstanding Assad ally Russia has accused the rebels of using chemical weapons.
Damascus has insisted any investigation should focus on the use of chemical weapons in Khan al-Assal in the northern province of Aleppo in March, which it blamed on the rebels.
The town was captured by the rebels from the army on Monday, in what diplomats at the United Nations said was a blow to the mission's hopes of gaining access.
The United Nations has received 13 allegations of the use of chemical weapons in Syria.
UN chief Ban Ki-moon is "gravely concerned" by the allegations, UN envoy on the Middle East peace process Robert Serry told the Security Council yesterday.
The United States has previously said that the use of chemical weapons in the Syrian conflict would constitute a "red line" that would warrant greater involvement.