Ould Zeidane, a former central bank governor and presidential contender, was appointed premier by Abdallahi earlier in the month and most of the new cabinet members have no previous association with Taya's rule or with the traditional political establishment.
Abderrahmane Ould Hamma Vezzaz, the economy and finance minister, previously worked with the Arab Bank for Economic Development in Africa (BADEA), founded by Arab League member states.
The oil and mines post -a significant portfolio in a country which became Africa's newest oil producer last year and is a big iron ore exporter - went to Mohamed El Moktar Ould Mohamed El Hacen, a specialist on extractive industries with the World Bank.
The new foreign minister is a former ambassador to Switzerland, Mohamed Saleck Ould Mohamed Lemine.
In an apparent gesture to black Mauritanians, who have long complained of discrimination and mistreatment at the hands of the traditional Moorish ruling elite, the job of interior minister went to Yall Zakaria, a black Mauritanian.
One of his tasks will be to organise the return of thousands of black Mauritanians who were expelled from the country during racial purges and killings committed between 1989 and 1991. Victims have called for compensation.
President Abdallahi, himself a Moor, says he will promote national unity and racial harmony, fight poverty and tackle outstanding social problems.
One of his stated priorities is eradicating slavery, which still exists in the largely desert Saharan state, most of whose population are nomads.
A descendant of freed slaves, Messaoud Ould Boulkheir, who finished fourth in last month's presidential election, was made president of the National Assembly this month.
Four ministerial posts in the new government went to Boulkheir's People's Progressive Alliance (APP) party, reflecting his support for Abdallahi in the decisive second round of the presidential poll.
The ministries that went to APP supporters included water and energy, agriculture and livestock, and youth and sports.
Abdallahi, a 69-year-old economist and former minister who won elections in March, was sworn in on April 19, sealing a democratic handover by the military officers.