Paralysed Paul Lamb and the family of the late Tony Nicklinson will appeal their unsuccessful challenges on the illegality of assisted suicide at the High Court.
The Lord Chief Justice, Lord Judge, and two other judges will hear the challenges today in the Court of Appeal.
Mr Nicklinson, 58, who suffered from locked-in syndrome, died on August 22 last year days after losing a landmark High Court right-to-die case.
Fifty-eight-year-old Paul Lamb, from Leeds, has joined forces with the family of Mr Nicklinson, who died in 2012, severely injured in a car accident in 1990, Mr Lamb no function in any of his limbs apart from a little movement in his right hand.
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Downpours keeping us on our toes today
The M20 in Kent has been closed in both directions after a pedestrian bridge allegedly collapsed on the motorway on Saturday.
The AA have warned of traffic jams and urged people to carry extra water in their vehicles because of the warm weather.