Votes are being counted after Mauritania's first election since last year's bloodless coup ended 20 years of authoritarian rule.
Turnout was reported to be high
Officials say two opposition groups - one representing former slaves - and the former ruling party are doing well in votes counted so far.
Observers say the poll passed off without incident.
Members of the military junta which seized power were banned from contesting the elections.
Turnout was said to be high and long queues formed even before polls opened.
"The vote functioned well throughout the country," said Marie-Anne Isler Beguin, head of the European Union's observer mission.
Voters were choosing 95 MPs and more than 200 local councils.
Military rule is due to end in March with presidential elections.
Slavery was formally abolished in Mauritania as recently as 1981.
The party of former slaves is reported to be doing well
The Progressive Popular Alliance (APP) was set up to represent them, saying they remained marginalised.
The Rally of Democratic Forces (RFD), led by well-known opposition leader Ahmed Ould Daddah, is also reported to be doing well, along with the Republican Party for Democracy and Renewal (PRDR), which governed the country prior to last year's coup.
After casting his vote, junta leader Colonel Ely Ould Mohamed Vall said he was "satisfied to see Mauritanians embark on the road to democracy and consequently on the way to economic development and political stability".
In June, turnout was also high in a referendum on a new constitution which, among other things, put a two-term limit on any future president.
At least 28 political parties were competing to be represented in the National Assembly - although only five parties were considered to be front-runners.
But Islamist parties and movements, considered to be among the most popular in the country, have been banned.
This has resulted in many Islamist candidates standing as independents.