David Norris and Gary Dobson are to appeal against their convictions for the racist murder of teenager Stephen Lawrence in south-east London in 1993.
Norris will appeal on the basis that the use in evidence of a surveillance video was unfair, his lawyer confirms.
The video showed him and Dobson using violent racist language.
Papers have also been received at the Court of Appeal from Dobson's solicitors, setting out his intention to appeal.
The pair were sentenced to life after being found guilty by an Old Bailey jury at the beginning of January.
Dobson was ordered to serve a minimum of 15 years and two months, and David Norris 14 years and three months.
Norris' lawyer said the appeal will be based on the grounds that about two thirds of the way through the trial what had been a scientific case about forensic evidence became a case about a surveillance video of the men.
He told BBC home affairs correspondent Tom Symonds this was unfair, because the case was about scientific evidence and the video could not prove Norris was at the scene of Stephen Lawrence's murder.
The police surveillance video, shot over several days in December 1994, showed the pair using racist language while they interacted with various friends and acquaintances.
During the Old Bailey trial, Dobson said he was "disgusted and embarrassed" by the language he had used as a teenager, while Norris apologised to the jury for having to listen to the comments, saying he was "ashamed".
Meanwhile, the Attorney General is reviewing the minimum terms given to the pair following a request from a member of the public and is due to report back in the next few days.
Dobson, 36, and Norris, 35, were the first people convicted over the fatal attack on Mr Lawrence by a group of white youths near a bus stop in Eltham on 22 April 1993.