Syrian refugees in Lebanon and Jordan are being given the chance to vote early in the presidential election due to be held next week.
The main polling stations opened at the Syrian embassies in Beirut and Amman on Wednesday.
The UN says 2.8 million Syrian refugees have fled to neighbouring countries.
President Bashar al-Assad is widely expected to win a third seven-year term in office in the 3 June election, which has been branded a farce by the West.
More than 160,000 people have died since the uprising against President Assad began in March 2011.
Thousands of Syrians have been flocking to their embassy in the hills overlooking Beirut.
At the scene - Jim Muir, BBC News, Beirut
The massive turnout for the expatriate Syrian vote at the embassy above Beirut produced scenes rarely observed at any embassy or polling station in the world.
At times it turned into a rowdy support rally for the incumbent Bashar al-Assad, with none of the normal election decorum.
As the only polling station available for the whole of Lebanon, and with probably 1.5m or more Syrians here, it was perhaps not surprising that the embassy was swamped. But the voting congestion brought much of Beirut to a halt, bringing home to many Lebanese how deeply embedded the Syrian crisis is here.
The strength and assertiveness of the vote may have reflected an underlying feeling among many Syrians abroad that the tide is running in the regime's favour, and it is time to climb aboard.
The opposition coalition welcomed President Obama's promises of more aid. But will it be enough to turn the tide, given Western reservations about the jihadi presence in rebel areas?
Half of the one million Syrian refugees registered in Lebanon are believed to be of voting age. Embassy officials say they may extend the time for voting if large numbers are unable to take part.
The poll in Jordan's capital Amman is being held days after the kingdom expelled the Syrian ambassador, Bahjat Suleiman, over what it called "repeated insults" against the country.
Voting also started at embassies in several other countries including Russia, Malaysia and Sudan on Wednesday, according to Syria's state-run Sana news agency.
The agency said the United Arab Emirates had banned Syrians there from voting, after similar moves by France, Germany and Belgium.
Many other expatriates live in countries where Syrian embassies have been closed since 2011.
This is the first time in decades that Syria is holding a presidential election with more than one candidate.
However, the other two candidates are not widely known and have been unable to campaign on an equal footing with the president, correspondents say.
Previous presidential terms have been called through a referendum with just one member of the Assad family on the ballot paper.