Judges in the European Court of Justice are to examine whether the UK can call EU leave without the consent of member states.
The UK will leave the EU on March 29 under the terms of "Article 50", which MPs sparked in March last year.
A group of Scottish politicians has introduced the court's challenge to find out if this can be abolished unilaterally.
The UK government has opposed the case being heard, but failed to stop going before judges in Luxembourg.
No ruling is expected immediately on Tuesday.
The case is being heard against the background of Prime Minister Theresa May is fighting to sell her draft bargain Brexit to MPs, before a vote in the Commons in December.
Those who pushed the court case said he could give MPs an additional option when considering whether the draft image should be approved or not, as he could keep the possibility of calling Brexit in completely on board.
The case was first raised in the names of a cross party group of Scottish politicians, including Andy Wightman and Ross Greer, MPE Alyn Smith and MPs Joanna Cherry MPs, and Labor MPs David Martin and Catherine Stihler.
They want the court to control whether the UK can abolish Article 50 unilaterally, and they have been allowed to take their case to Luxembourg by the Court of the Scottish Session.
Mr Wightman said he was looking forward to the hearing, adding: "The question that MPs can delete Unilateral Article 50 is essential, as the disorder around Brexit does not show any sign of resolved.
"The United Kingdom parliament must be fully informed of all its options."
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Ms Cherry raised the case and the issue of abolishing Article 50 with Mrs. May in Commons on Monday, urging the prime minister to say "it will not happen because it is not a government policy".
The UK government has always fought the case, arguing in the supreme courts of Scotland and the UK that it should not have been referred to European judges.
The UK government's view is that the court has "long rejected for very good reasons" not to answer theoretical questions, and because ministers do not intend to abolish Article 50, the question of whether they are capable be theoretical or not.
He has also argued that the questions are being given to the court "for political debate purposes", and "has been designed to influence the terms of debate that have yet to be found in the parliament ".