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, the BBC's Jim Muir reports from the scene.
Half of the one million Syrian refugees registered in Lebanon are believed to be of voting age.
But there is only one polling station and the facilities appear insufficient to cope with the large numbers coming in, our correspondent says, Lina Sinjab reports from the Bekaa Valley and speaks to Syrian refugees.
Embassy officials say they may extend the time for voting if large numbers are unable to take part.
Supporters of President Assad's government will be keen to demonstrate their loyalty, our correspondent says.
Others who are not hardcore backers of the opposition may feel the government is going to survive, and fear they will not be able to return home if they do not vote.
The poll in Jordan comes 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.