The Crown Office has applied to the High Court to set aside the acquittals of Ronnie Coulter, Andrew Coulter and David Montgomery, and prosecute them again over the death of Surjit Singh Chhokar.
The 32-year-old was killed in Overtown, North Lanarkshire, in November 1998.
The murder had sparked controversy after the failure of authorities to secure a conviction for the killing despite the arrests of three men and two subsequent trials.
A statement from the Crown Office said: "The Lord Advocate, Frank Mulholland QC, has today applied to the High Court for authority under the Double Jeopardy (Scotland) Act 2011 to set aside the acquittal of Ronnie Coulter, Andrew Coulter and David Montgomery, and prosecute them again for the murder of Surjit Singh Chhokar."
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Two official inquiries were ordered in the wake of the original trials over Chhokar's death and one made allegations of "institutional racism".
In January 2012, police said they had been instructed by the Crown Office to carry out a new investigation into the unsolved murder.
Solicitor Aamer Anwar, representing the family, said: "There still remains significant legal hurdles to be overcome. The Chhokar family are grateful to the Crown Office and Police Scotland for their determination and support. Today is an important step but the Chhokar family will only ever be at peace when there is justice."
Under the Scottish Act, a suspect can now face retrial for a very serious crime if "compelling new evidence" has emerged.