A challenge by a third man, whose case was rejected at the High Court on the same day as Mr Nicklinson's, will also be heard today.
The locked-in syndrome sufferer, who cannot be identified for legal reasons but is referred to as "Martin", suffered a massive stroke in August 2008.
He is unable to speak and virtually unable to move, describing his life as "undignified, distressing and intolerable", and wants to be allowed a "dignified suicide".
More top news
Drinking three to five cups of coffee a day could reduce the risk of clogged arteries and thus heart attacks, a study has found.
There are five million British expats across the globe. Many have a vested interest in May's election and many still have the right to vote.
Abba's Bjorn Ulvaeus has a boyish enthusiasm for the cashless society - and he has a challenge for ITV News viewers.