The eight -- Austria, Greece, Hungary, Italy, Luxembourg, Romania, Slovenia and Spain -- sent official letters to the European Commission, which will draw up a plan for them to work more closely together.
It is the first time the procedure -- known in Brussels as "enhanced cooperation" -- has been used in the European Union.
"The procedure has been launched. We will have to wait and see if other countries will rally to it, to create enough momentum," the diplomat said.
The commission, the EU's executive body, said Wednesday that it had not yet received the letters, in a move made necessary after Sweden resisted all attempts to harmonise divorce laws across the 27-nation bloc.
Around 170,000 couples from different nations divorce each year but the EU has struggled to help end fighting over which court should settle their separation, at an often difficult and emotional time.
Sweden strives to expedite divorces as quickly as possible, while the process can take far longer elsewhere, with some nations demanding a period of separation before any court divorce can begin.
Laws are tougher than most in Poland and Ireland, while Malta does not recognise the right to divorce at all. Adultery is recognised in courts in France, but not in Finland.
Marriage between homosexuals is only recognised in a few member states.
France is known to strongly back the move by the eight, while Belgium, Germany, Lithuania, Portugal and Slovakia are thinking about joining them, according to EU officials.
The Czech Republic, Finland, Latvia and Poland are opposed, along with Estonia which fears that the idea of a two-speed Europe would "open up a Pandora's box" in other areas.
EU Justice Commissioner Jacques Barrot said that he wanted to examine "all the consequences that will arise" from the move, which still must be approved by two thirds of the member nations for the eight to be able to forge ahead.